TRANSMITTER APPARATUS AND SIGNAL PROCESSING METHOD THEREOF

Abstract

A transmitter apparatus and a receiver apparatus are provided. The transmitter apparatus includes: an encoder configured to generate a low density parity check (LDPC) by performing LDPC encoding; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol. The modulator maps a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol.

Description

BACKGROUND

1. Technical Field

Apparatuses and methods consistent with exemplary embodiments relate to a transmitter apparatus and a signal processing method thereof, and more particularly, to a transmitter apparatus which processes data and transmits the data, and a signal processing method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcasting communication services are moving into the era of digitalization, multi-channel, wideband, and high quality. In particular, as more high quality digital televisions, portable multimedia players (PMPs) and portable broadcasting equipment are used in recent years, there is an increasing demand for various methods for receiving digital broadcasting services.

Many standard groups have established various standards to meet such a demand for providing a variety of services to satisfy the user's needs. Still, however, there is a demand for a method for providing an improved service with more robust encoding and decoding performance.

SUMMARY

One or more exemplary embodiments may overcome the above disadvantages and other disadvantages not described above. However, it is understood that one or more exemplary embodiment are not required to overcome the disadvantages described above, and may not overcome any of the problems described above.

One or more exemplary embodiments provide a transmitter apparatus which can map a bit included in a predetermined group from among a plurality of groups of a Low Density Parity Check (LDPC) codeword onto a predetermined bit of a modulation symbol, and transmit the bit, and a signal processing method thereof.

According to an aspect of an exemplary embodiment, there is provided a transmitter apparatus including: an encoder configured to generate an LDPC codeword by performing LDPC encoding; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator maps a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol.

Each of the plurality of groups may be formed of 360 bits.

The interleaver may include: a parity interleaver configured to interleave parity bits constituting the LDPC codeword; a group interleaver configured to perform group-interleaving by dividing the parity-interleaved LDPC codeword into the plurality of groups and rearranging an order of the plurality of groups in; and a block interleaver configured to perform block-interleaving of the plurality of groups the order of which has been rearranged.

The group interleaver may rearrange the order of the plurality of groups based on Equation 11.

In Equation 11, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method and a code rate.

The π(j) may be defined as in Table 37 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15.

The π(j) may be defined as in Table 38 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15.

The π(j) may be defined as in Table 39 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 40 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 41 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15.

The block interleaver may perform the block-interleaving by writing the plurality of groups in each of a plurality of columns in group units in a column direction, and reading each row of the plurality of columns in which the plurality of groups are written in group units in a row direction.

The block interleaver, for the writing the plurality of groups in each of the plurality of columns, may divide the plurality of columns in at least two parts, write at least some groups among the plurality of groups in a first part of each of the plurality of columns serially, and write the remaining of the plurality of groups in the other part of each of the plurality of columns.

The group interleaver may rearrange the order of the plurality of groups such that groups including a bit to be mapped onto a same location of different modulation symbols are serially arranged to be adjacent to one another so that the block interleaver writes a predetermined group among the plurality of groups in a predetermined column among the plurality of columns.

The modulator may generate the modulation symbol by mapping a bit output from the predetermined column onto a predetermined bit in the modulation symbol.

According to an aspect of another exemplary embodiment, there is provided a signal processing method of a transmitter apparatus, the signal processing method including: generating an LDPC codeword by performing LDPC encoding; interleaving the LDPC codeword; and mapping the interleaved LDPC codeword onto a modulation symbol, wherein the mapping the interleaved LDPC codeword onto the modulation symbol includes mapping a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol.

Each of the plurality of groups may be formed of 360 bits.

The interleaving may include: interleaving parity bits constituting the LDPC codeword; group-interleaving by dividing the parity-interleaved LDPC codeword into the plurality of groups and rearranging an order of the plurality of groups; and block-interleaving the plurality of groups the order of which has been rearranged.

The rearranging the order of the plurality of groups in the group-wise fashion may include rearranging the order of the plurality of groups in the group-wise fashion based on Equation 11.

In Equation 11, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

The π(j) may be defined as in Table 37 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15.

The π(j) may be defined as in Table 38 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15.

The π(j) may be defined as in Table 39 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 40 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 41 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15.

The block-interleaving the plurality of groups may include: performing the block-interleaving by writing the plurality of groups in each of a plurality of columns in group units in a column direction; and reading each row of the plurality of columns in which the plurality of groups are written in group units in a row direction.

The block-interleaving the plurality of groups may include: dividing the plurality of columns in at least two parts; writing at least some groups among the plurality of groups in a first part of each of the plurality of columns serially; and writing the remaining of the plurality of groups in the other part of each of the plurality of columns.

The rearranging the order of the plurality of groups on the group-wise fashion may be performed such that groups comprising a bit to be mapped onto a same location of different modulation symbols are serially arranged to be adjacent to one another so that a predetermined group among the plurality of groups is written on a predetermined column among the plurality of columns.

The mapping the LDPC codeword onto the modulation symbol may include generating the modulation symbol by mapping a bit output from the predetermined column onto a predetermined bit in the modulation symbol.

According to various exemplary embodiments described above, improved decoding and receiving performance maybe provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing in detail exemplary embodiments, with reference to the accompanying drawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of a transmitter apparatus according to an exemplary embodiment;

FIGS. 2 and 3 are views to illustrate a configuration of a parity check matrix according to exemplary embodiments;

FIG. 4 is a block diagram to illustrate a configuration of an interleaver according to an exemplary embodiment;

FIGS. 5 to 7 are views illustrating a method for processing an LDPC codeword on a group basis according to exemplary embodiments;

FIGS. 8 to 11 are views to illustrate a configuration of a block interleaver and an interleaving method according to exemplary embodiments;

FIGS. 12 and 13 are views to illustrate an operation of a demultiplexer according to exemplary embodiments;

FIG. 14 is a view to illustrate an example of a uniform constellation modulation method according to an exemplary embodiment;

FIGS. 15 to 19 are views to illustrate an example of a non-uniform constellation modulation method according to exemplary embodiments;

FIGS. 20 to 22 are views to illustrate performance when a signal processing method according to exemplary embodiments are applied;

FIG. 23 is a block diagram to illustrate a configuration of an interleaver according to another exemplary embodiment;

FIGS. 24 to 26 are views to illustrate a configuration of a block-row interleaver and an interleaving method according to exemplary embodiments;

FIG. 27 is a block diagram to illustrate a configuration of a receiver apparatus according to an exemplary embodiment;

FIGS. 28 and 29 are block diagrams to illustrate a configuration of a deinterleaver according to exemplary embodiments;

FIG. 30 is a flowchart to illustrate a signal processing method according to an exemplary embodiment; and

FIG. 31 is a view provided to explain a block deinterleaver according to an exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greater detail with reference to the accompanying drawings.

In the following description, same reference numerals are used for the same elements when they are depicted in different drawings. The matters defined in the description, such as detailed construction and elements, are provided to assist in a comprehensive understanding of the exemplary embodiments. Thus, it is apparent that the exemplary embodiments can be carried out without those specifically defined matters. Also, functions or elements known in the related art are not described in detail since they would obscure the exemplary embodiments with unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of a transmitter apparatus according to an exemplary embodiment. Referring to FIG. 1, the transmitter apparatus 100 includes an encoder 110, an interleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a Low Density Parity Check (LDPC) codeword by performing LDPC encoding. The encoder 110 may include an LDPC encoder (not shown) to perform the LDPC encoding.

Specifically, the encoder 110 LDPC-encodes input bits to information word bits to generate the LDPC codeword which is formed of the information word bits and parity bits (that is, LDPC parity bits). Here, since an LDPC code for the LDPC encoding is a systematic code, the information word bits may be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the parity bits. For example, the LDPC codeword is formed of N_ldpc number of bits, and includes K_ldpc number of information word bits and N_parity=N_ldpc−K_ldpc number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword by performing the LDPC encoding based on a parity check matrix. That is, since the LDPC encoding is a process for generating an LDPC codeword to satisfy H·C^T=0, the encoder 110 may use the parity check matrix when performing the LDPC encoding. Herein, H is a parity check matrix and C is an LDPC codeword.

For the LDPC encoding, the transmitter apparatus 100 may include a separate memory and may pre-store parity check matrices of various formats.

For example, the transmitter apparatus 100 may pre-store parity check matrices which are defined in Digital Video Broadcasting-Cable version 2 (DVB-C2), Digital Video Broadcasting-Satellite-Second Generation (DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial (DVB-T2), etc., or may pre-store parity check matrices which are defined in the North America digital broadcasting standard system Advanced Television System Committee (ATSC) 3.0 standards, which are currently being established. However, this is merely an example and the transmitter apparatus 100 may pre-store parity check matrices of other formats in addition to these parity check matrices.

Hereinafter, a configuration of a parity check matrix will be explained in detail with reference to FIGS. 2 and 3.

First, referring to FIG. 2, a parity check matrix 200 is formed of an information word submatrix 210 corresponding to information word bits, and a parity submatrix 220 corresponding to parity bits. In the parity check matrix 200, elements other than elements with 1 have 0.

The information word submatrix 210 includes K_ldpc number of columns and the parity submatrix 220 includes N_parity=N_ldpc−K_ldpc number of columns. The number of rows of the parity check matrix 200 is identical to the number of columns of the parity submatrix 220, N_parity=N_ldpc−K_ldpc.

In addition, in the parity check matrix 200, N_ldpc is a length of an LDPC codeword, K_ldpc is a length of information word bits, and N_parity=N_ldpc−K_ldpc is a length of parity bits. The length of the LDPC codeword, the information word bits, and the parity bits mean the number of bits included in each of the LDPC codeword, the information bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 and the parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_ldpc number of columns (that is, 0^th column to (K_ldpc−1)^th column), and follows the following rules:

First, M number of columns from among K_ldpc number of columns of the information word submatrix 210 belong to the same group, and K_ldpc number of columns is divided into K_ldpc/M number of column groups. In each column group, a column is cyclic-shifted from an immediately previous column by Q_ldpc or Q_ldpc number of bits.

Herein, M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix 210 (e.g., M=360), and Q_ldpc is a size by which one column is cyclic-shifted from an immediately previous column in a same column group in the information word submatrix 210. M and Q_ldpc are integers and are determined to satisfy Q_ldpc=(N_ldpc−K_ldpc)/M. In this case, K_ldpc/M is also an integer. M and Q_ldpc may have various values according to a length of the LDPC codeword and a code rate.

For example, when M=360 and the length of the LDPC codeword, N_ldpc, is 64800, Q_ldpc may be defined as in table 1 presented below, and, when M=360 and the length N_ldpc of the LDPC codeword is 16200, Q_ldpc may be defined as in table 2 presented below.

	TABLE 1
	Code Rate	Nldpc	M	Qldpc
	5/15	64800	360	120
	6/15	64800	360	108
	7/15	64800	360	96
	8/15	64800	360	84
	9/15	64800	360	72
	10/15	64800	360	60
	11/15	64800	360	48
	12/15	64800	360	36
	13/15	64800	360	24

	TABLE 2
	Code Rate	Nldpc	M	Qldpc
	5/15	16200	360	30
	6/15	16200	360	27
	7/15	16200	360	24
	8/15	16200	360	21
	9/15	16200	360	18
	10/15	16200	360	15
	11/15	16200	360	12
	12/15	16200	360	9
	13/15	16200	360	6

Second, when the degree of the 0^th column of the i^th column group (i=0, 1, . . . , K_ldpc/M−1) is D_i (herein, the degree is the number of value 1 existing in each column and all columns belonging to the same column group have the same degree), and a position (or an index) of each row where 1 exists in the 0^th column of the i^th column group is R_i,0⁽⁰⁾, R_i,0⁽¹⁾, . . . , R_i,0^(Di−1), an index R_i,j^(k) of a row where k^th weight-1 is located in the j^th column in the i^th column group (that is, an index of a row where k^th 1 is located in the j^th column in the i^th column group) is determined by following Equation 1:

R _i,j ^(k) =R _i,(j-1) ^(k) +Q _ldpc mod(N_ldpc−K_ldpc)  (1)

where k=0, 1, 2, . . . D_i−1; i=0, 1, . . . , K_ldpc/M−1; and j=1, 2, . . . , M−1.

Equation 1 can be expressed as following Equation 2:

R _i,j ^(k) ={R _i,0 ^(k)+(j mod M)×Q_ldpc} mod(N_ldpc−K_ldpc)  (2)

where k=0, 1, 2, . . . D_i−1; i=0, 1, . . . , K_ldpc/M−1; and j=1, 2, . . . , M−1.

In the above equations, R_i,j^(k) is an index of a row where k^th weight-1 is located in the j^th column in the i^th column group, N_ldpc is a length of an LDPC codeword, K_ldpc is a length of information word bits, D_i is a degree of columns belonging to the i^th column group, M is the number of columns belonging to a single column group, and Q_ldpc is a size by which each column in the column group is cyclic-shifted.

As a result, referring to these equations, when only R_i,0^(k) is known, the index R_i,j^(k) of the row where the k^th weight-1 is located in the j^th column in the i^th column group can be known. Therefore, when the index value of the row where the k^th weight-1 is located in the first column of each column group is stored, a position of column and row where weight-1 is located in the parity check matrix 200 having the configuration of FIG. 2 (that is, in the information word submatrix 210 of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging to the i^th column group have the same degree D_i. Accordingly, the LDPC codeword which stores information on the parity check matrix according to the above-described rules may be briefly expressed as follows.

For example, when N_ldpc is 30, K_ldpc is 15, and Q_ldpc is 3, position information of the row where weight-1 is located in the 0^th column of the three column groups may be expressed by a sequence of Equations 3 and may be referred to as “weight-1 position sequence”.

R _1,0 ⁽¹⁾=1,R_1,0⁽²⁾=2,R_1,0⁽³⁾=8,R_1,0⁽⁴⁾=10,

R _2,0 ⁽¹⁾=0,R_2,0⁽²⁾=9,R_1,0⁽³⁾=13,

R _3,0 ⁽¹⁾=0,R_3,0⁽²⁾=14.  (3),

where R_i,j^(k) is an index of a row where k^th weight-1 is located in the j^th column in the i^th column group.

The weight-1 position sequence like Equation 3 which expresses an index of a row where 1 is located in the 0^th column of each column group may be briefly expressed as in Table 3 presented below:

TABLE 3
1 2 8 10
0 9 13
0 14

Table 3 shows positions of elements having weight-1, that is, the value 1, in the parity check matrix, and the i^th weight-1 position sequence is expressed by indexes of rows where weight-1 is located in the 0^th column belonging to the i^th column group.

The information word submatrix 210 of the parity check matrix according to an exemplary embodiment may be defined as in Tables 4 to 26 presented below, based on the above descriptions.

Specifically, Tables 4 to 26 show indexes of rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210. That is, the information word submatrix 210 is formed of a plurality of column groups each including M number of columns, and positions of 1 in the 0^th column of each of the plurality of column groups may be defined by Tables 4 to 26.

Herein, the indexes of the rows where 1 is located in the 0^th column of the i^th column group mean “addresses of parity bit accumulators”. The “addresses of parity bit accumulators” have the same meaning as defined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards which are currently being established, and thus, a detailed explanation thereof is omitted.

For example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 4 presented below:

TABLE 4
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  245 449 491 980 1064 1194 1277 1671 2026 3186 4399 4900 5283
   5413 5558 6570 7492 7768 7837 7984 8306 8483 8685 9357 9642
   10045 10179 10261 10338 10412
1  1318 1584 1682 1860 1954 2000 2062 3387 3441 3879 3931 4240
   4302 4446 4603 5117 5588 5675 5793 5955 6097 6221 6449 6616
   7218 7394 9535 9896 10009 10763
2  105 472 785 911 1168 1450 2550 2851 3277 3624 4128 4460 4572
   4669 4783 5102 5133 5199 5905 6647 7028 7086 7703 8121 8217
   9149 9304 9476 9736 9884
3  1217 5338 5737 8334
4  855 994 2979 9443
5  7506 7811 9212 9982
6  848 3313 3380 3990
7  2095 4113 4620 9946
8  1488 2396 6130 7483
9  1002 2241 7067 10418
10 2008 3199 7215 7502
11 1161 7705 8194 8534
12 2316 4803 8649 9359
13 125 1880 3177
14 1141 8033 9072

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 5 presented below:

TABLE 5
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  13 88 136 188 398 794 855 918 954 1950 2762 2837 2847 4209 4342
   5092 5334 5498 5731 5837 6150 6942 7127 7402 7936 8235 8307
   8600 9001 9419 9442 9710
1  619 792 1002 1148 1528 1533 1925 2207 2766 3021 3267 3593 3947
   4832 4873 5109 5488 5882 6079 6097 6276 6499 6584 6738
   6795 7550 7723 7786 8732 9060 9270 9401
2  499 717 1551 1791 2535 3135 3582 3813 4047 4309 5126 5186 5219
   5716 5977 6236 6406 6586 6591 7085 7199 7485 7726 7878
   8027 8066 8425 8802 9309 9464 9553 9671
3  658 4058 7824 8512
4  3245 4743 8117 9369
5  465 6559 8112 9461
6  975 2368 4444 6095
7  4128 5993 9182 9473
8  9 3822 5306 5320
9  4 8311 9571 9669
10 13 8122 8949 9656
11 3353 4449 5829 8053
12 7885 9118 9674
13 7575 9591 9670
14 431 8123 9271
15 4228 7587 9270
16 8847 9146 9556
17 11 5213 7763

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 6 presented below:

TABLE 6
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  432 655 893 942 1285 1427 1738 2199 2441 2565 2932 3201 4144
   4419 4678 4963 5423 5922 6433 6564 6656 7478 7514 7892
1  220 453 690 826 1116 1425 1488 1901 3119 3182 3568 3800 3953
   4071 4782 5038 5555 6836 6871 7131 7609 7850 8317 8443
2  300 454 497 930 1757 2145 2314 2372 2467 2819 3191 3256 3699
   3984 4538 4965 5461 5742 5912 6135 6649 7636 8078 8455
3  24 65 565 609 990 1319 1394 1465 1918 1976 2463 2987 3330 3677
   4195 4240 4947 5372 6453 6950 7066 8412 8500 8599
4  1373 4668 5324 7777
5  189 3930 5766 6877
6  3 2961 4207 5747
7  1108 4768 6743 7106
8  1282 2274 2750 6204
9  2279 2587 2737 6344
10 2889 3164 7275 8040
11 133 2734 5081 8386
12 437 3203 7121
13 4280 7128 8490
14 619 4563 6206
15 2799 6814 6991
16 244 4212 5925
17 1719 7657 8554
18 53 1895 6685
19 584 5420 6856
20 2958 5834 8103

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 7, 8 or 9 presented below:

TABLE 7
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  32 384 430 591 1296 1976 1999 2137 2175 3638 4214 4304 4486
   4662 4999 5174 5700 6969 7115 7138 7189
1  1788 1881 1910 2724 4504 4928 4973 5616 5686 5718 5846 6523
   6893 6994 7074 7100 7277 7399 7476 7480 7537
2  2791 2824 2927 4196 4298 4800 4948 5361 5401 5688 5818 5862
   5969 6029 6244 6645 6962 7203 7302 7454 7534
3  574 1461 1826 2056 2069 2387 2794 3349 3366 4951 5826 5834
   5903 6640 6762 6786 6859 7043 7418 7431 7554
4  14 178 675 823 890 930 1209 1311 2898 4339 4600 5203 6485 6549
   6970 7208 7218 7298 7454 7457 7462
5  4075 4188 7313 7553
6  5145 6018 7148 7507
7  3198 4858 6983 7033
8  3170 5126 5625 6901
9  2839 6093 7071 7450
10 11 3735 5413
11 2497 5400 7238
12 2067 5172 5714
13 1889 7173 7329
14 1795 2773 3499
15 2695 2944 6735
16 3221 4625 5897
17 1690 6122 6816
18 5013 6839 7358
19 1601 6849 7415
20 2180 7389 7543
21 2121 6838 7054
22 1948 3109 5046
23 272 1015 7464

TABLE 8
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  5 519 825 1871 2098 2478 2659 2820 3200 3294 3650 3804 3949
   4426 4460 4503 4568 4590 4949 5219 5662 5738 5905 5911
   6160 6404 6637 6708 6737 6814 7263 7412
1  81 391 1272 1633 2062 2882 3443 3503 3535 3908 4033 4163 4490
   4929 5262 5399 5576 5768 5910 6331 6430 6844 6867 7201
   7274 7290 7343 7350 7378 7387 7440 7554
2  105 975 3421 3480 4120 4444 5957 5971 6119 6617 6761 6810
   7067 7353
3  6 138 485 1444 1512 2615 2990 3109 5604 6435 6513 6632 6704
   7507
4  20 858 1051 2539 3049 5162 5308 6158 6391 6604 6744 7071
   7195 7238
5  1140 5838 6203 6748
6  6282 6466 6481 6638
7  2346 2592 5436 7487
8  2219 3897 5896 7528
9  2897 6028 7018
10 1285 1863 5324
11 3075 6005 6466
12 5 6020 7551
13 2121 3751 7507
14 4027 5488 7542
15 2 6012 7011
16 3823 5531 5687
17 1379 2262 5297
18 1882 7498 7551
19 3749 4806 7227
20 2 2074 6898
21 17 616 7482
22 9 6823 7480
23 5195 5880 7559

TABLE 9
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  6 243 617 697 1380 1504 1864 1874 1883 2075 2122 2439 2489
   3076 3715 3719 3824 4028 4807 5006 5196 5532 5688 5881 6216
   6899 7000 7118 7284 7412 7417 7523
1  0 6 17 20 105 1279 2443 2523 2800 3458 3684 4257 4799 4819
   5499 5665 5810 5927 6169 6536 6617 6669 7069 7127 7132 7158
   7164 7230 7320 7393 7396 7465
2  2 6 12 15 2033 2125 3352 3382 5931 7024 7143 7358 7391 7504
3  5 17 1725 1932 3277 4781 4888 6025 6374 7001 7139 7510 7524
   7548
4  4 19 101 1493 4111 4163 4599 6517 6604 6948 6963 7008 7280
   7319
5  8 28 2289 5025
6  5505 5693 6844 7552
7  9 3441 7424 7533
8  917 1816 3540 4552
9  256 6362 6868
10 2125 3144 5576
11 3443 5553 7201
12 2219 3897 4541
13 6331 6481 7224
14 7 1444 5568
15 81 1325 3345
16 778 2726 7316
17 3512 6462 7259
18 768 3751 6028
19 4665 7130 7452
20 2375 6814 7450
21 7073 7209 7483
22 2592 6466 7018
23 3716 5838 7547

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 10 presented below:

TABLE 10
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  350 462 1291 1383 1821 2235 2493 3328 3353 3772 3872 3923 4259
   4426 4542 4972 5347 6217 6246 6332 6386
1  177 869 1214 1253 1398 1482 1737 2014 2161 2331 3108 3297 3438
   4388 4430 4456 4522 4783 5273 6037 6395
2  347 501 658 966 1622 1659 1934 2117 2527 3168 3231 3379 3427
   3739 4218 4497 4894 5000 5167 5728 5975
3  319 398 599 1143 1796 3198 3521 3886 4139 4453 4556 4636 4688
   4753 4986 5199 5224 5496 5698 5724 6123
4  162 257 304 524 945 1695 1855 2527 2780 2902 2958 3439 3484
   4224 4769 4928 5156 5303 5971 6358 6477
5  807 1695 2941 4276
6  2652 2857 4660 6358
7  329 2100 2412 3632
8  1151 1231 3872 4869
9  1561 3565 5138 5303
10 407 794 1455
11 3438 5683 5749
12 1504 1985 3563
13 440 5021 6321
14 194 3645 5923
15 1217 1462 6422
16 1212 4715 5973
17 4098 5100 5642
18 5512 5857 6226
19 2583 5506 5933
20 784 1801 4890
21 4734 4779 4875
22 938 5081 5377
23 127 4125 4704
24 1244 2178 3352
25 3659 6350 6465
26 1686 3464 4336

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 10/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 11, 12 or 13 presented below:

TABLE 11
   Index of row
i  where 1 is located in the 0th column of the ith column group
0  76 545 1005 1029 1390 1970 2525 2971 3448 3845 4088 4114 4163
   4373 4640 4705 4970 5094
1  14 463 600 1676 2239 2319 2326 2815 2887 4278 4457 4493 4597
   4918 4989 5038 5261 5384
2  451 632 829 1006 1530 1723 2205 2587 2801 3041 3849 4382 4595
   4727 5006 5156 5224 5286
3  211 265 1293 1777 1926 2214 2909 2957 3178 3278 3771 4547
   4563 4737 4879 5068 5232 5344
4  6 2901 3925 5384
5  2858 4152 5006 5202
6  9 1232 2063 2768
7  7 11 2781 3871
8  12 2161 2820 4078
9  3 3510 4668 5323
10 253 411 3215 5241
11 3919 4789 5040 5302
12 12 5113 5256 5352
13 9 1461 4004 5241
14 1688 3585 4480 5394
15 8 2127 3469 4360
16 2827 4049 5084 5379
17 1770 3331 5315 5386
18 1885 2817 4900 5088
19 2568 3854 4660
20 1604 3565 5373
21 2317 4636 5156
22 2480 2816 4094
23 14 4518 4826
24 127 1192 3872
25 93 2282 3663
26 2962 5085 5314
27 2078 4277 5089
28 9 5280 5292
29 50 2847 4742

TABLE 12
i  Index of row where 1 is located in the 0th column of the ith column group
0  44  449 544 788 992 1389 1800 1933 2461 2975 3186 3442 3733 3773 4076 4308 4323 4 05 48 2 5034 5080 5135 5146 5269 53 7
1  25 113 1 9 147 307 10  1078 1572 1773 1957 214  2609 2642 2901 3371 3414 3935 4141 4165 4271 4520 4754 4971 5160 5179
2  341 424 1375 1559 1953 2577 2721 3257 3706 4025 4273 4689 4995 5005
3  442 465 1892 2274 2292 2999 3156 3308 3883 4084 4516 4636 4743 5200
4  22 1809 2406 3332 3359 3430 3466 4 10 4638 5224 5280 5288 5337 5381
5  29 120  1444 1720 1836 2138 2902 3601 3647 4138 4269 4457 4 65 5 15
6  1138 249 0  852 4 02
7  3050 53 1 5 6
8  278 399 4810
9  1200 3571 4 04
10 1705 2811 344
11 2180 4242 5336
12 4539 5069 5363
13 3318 3645 4427
14 2902 5134 5176
15 5123 5130 5229
16 47 4474 5 6
17 2399 3981 5067
18 2377 2465 5080
19 1413 2471 5326
20 2502 4911 5329
21 4770 5139 5356
22 3263 4000 4022
23 648 2015 4867
24 311 2 09 406
25 1284 3246 3740
26 1080 3820
27 1261 2408 4608
28 3838 4076 4842
29 2294 4592 5254
indicates data missing or illegible when filed

TABLE 13
i  Index of row where 1 is located in the 0th column of the ith column group
0  352 747 894 1437 1688 1807 1883 2119 2159 3321 3400 3543 3588 3770 3821 4384 4470 4884 5012 5036 5084 5101 5271 5281 5353
1  505 3915 1156 1269 1518 1650 2153 2256 2344 2465 2509 2867 2875 3007 3254 3519 3687 4331 4439 4532 4940 5011 507 6 5113 5367
2  26  346 650 919 12 0 4389 4653 4721 4838 5054 5157 5162 5275 5362
3  220 236 828 1590 1792 3259 3647 4276 4281 4325 4963 4974 5003 5037
4  381 737 1099 1409 2364 2955 3228 3341 3473 3985 4257 4730 5173 5242
5  88 771 1640 1737 1803 2408 2575 2974 3167 3464 3780 4501 4901 5047
6  749 1502 2201 3189
7  2873 3245 3427
8  2158 2605 3165
9  1 3438 3 06
10 10 3019 5221
11 371 2901 2923
12 9 3935 4683
13 1937 3502 3735
14 507 3128 4994
15 25  854 4550
16 1178 4737 5366
17 2 223 5304
18 1146 5175 5197
19 1816 2313 3649
20 740 1951 3844
21 1320 3703 4791
22 1754 2905 40 8
23 7 917 5277
24 1048 3954 5396
25 4804 4824 5105
26 2812 3895 5226
27 0 5318 5358
28 1483 2324 4826
29 2266 4752 5387
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 11/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 14 presented below:

TABLE 14
i  Index of row where 1 is located in the 0th column of the ith column group
0  108 297 703 742 1345 1443 1495 1628 1812 2341 255  2669 2810 2877 3442 3690 3755 3904 4264
1  180 211 477 788 824 1090 1272 1578 1685 1948 2050 2195 2233 2546 2757 2946 3147 3299 3544
2  627 741 1135 1157 1226 1333 1378 1427 1454 1696 1757 1772 2099 2208 2592 3354 3580 4066 4242
3  9 79  959 989 1006 1032 1135 1209 1382 1484 1703 1855 1985 2043 2629 2845 3136 3450 3742
4  230 413 801 829 1108 1170 1291 1759 1793 1827 1976 2000 2423 2466 2917 3010 3600 3782 4143
5  56 142 236 381 1050 1141 1372 1627 1985 2247 2340 3023 3434 3519 3957 4013 4142 4164 4279
6  298 1211 2548 3643
7  73 1070 1614 1748
8  1439 2141 3614
9  284 1564 2629
10 607 660 855
11 1195 2037 2753
12 49 1198 2562
13 296 1145 3540
14 1516 2315 2382
15 154 722 4016
16 759 2375 3825
17 162 194 1749
18 2335 2422 2632
19 6 1172 2583
20 726 1325 1428
21 985 2708 2769
22 255 2801 3181
23 2979 3720 4090
24 208 1428 4094
25 199 3743 3757
26 1229 2059 4282
27 458 1100 1387
28 1199 2481 3284
29 1161 1467 4060
30 959 3014 4144
31 2666 3960 4125
32 2809 3834 4318
indicates data missing or illegible when filed

In another example, when the length Nldpc of the LDPC codeword is 16200, the code rate R is 12/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 15 or 16 presented below:

TABLE 15
   Index of row where 1 is located in the 0th column of the ith column group
0  3 394 1014 1214 1361 1477 1534 1660 1856 2745 2987 2991 3124 3155
1  59 136 528 781 803 928 1293 148  1944 2041 2200 2 13 2690 2847
2  155 24  311 621 1114 12 9 1281 1783 1995 2047 2672 2803 2885 3014
3  79 870 974 1326 1449 1531 2077 2317 2467 2627 2811 3083 3101 3132
4  4 582 660 902 1048 1482 1697 1744 1928 2628 2699 2728 3045 3104
5  175 3 95 429 1027 10  1068 1154 1158 11 5 2147 2359 2376 2 13 2 82
6  1388 2241 3118 3148
7  143 506 2057 3148
8  1594 2217 2705
9  398 988 2551
10 1149 2588 2654
11 67  2844 3115
12 1508 1547 1954
13 1199 1267 1710
14 2589 3163 3207
15 1 2583 2974
16 2766 2897 3166
17 929 1823 2742
18 1113 3007 3239
19 1753 2478 31
20 0 509 1811
21 1672  64  2984
22 9 5 14 2 3230
23 3 1077 2917
24 1183 1316 1662
25 96  15 3 3233 9
26 64 1996 222
27 1442 2 58 3181
28 513 973 1058
29 1263 3185  229
30 681 13 4  017
31 419 2853 3217
32 3 2404 317
33 2 17 27 2 2854
34 1879 2940 3235
35 6 7 1704 30 0
indicates data missing or illegible when filed

TABLE 16
   Index of row where 1 is located in the 0th column of the ith column group
0  69 170 550 11 7 1190 1250 1 09 14  1 12 1 25 2091 241  2580 2 7  29  2995  175  2 4
1  299 652  80 732 11 7 1 94 1779 1 4  1  220  22  22  2  27  32   22
2  107 133 351  40  5 11  1175 1479 1 7 20  2139 2586 2 9 2  2  2
3  75 458    46     8  194  2  2471 2574 2715  00  3
4  0 7 897 1664 19 1 2172 2268 2272 2364 287  2902   3  3121 32  3
5  121  99  0 11 7  16 1  17  1  1  21 0  5   74  2949 3001 30  3152
6  97 2022 2 26 2 7
7  72 232  2504 3
8  8 1 1 4 321  32
9  1807 2918  178
10 671 120  2343
11 405 490 3212
12 1 1474 3235
13 527 1224 2139
14 3 1997 29 2
15 23  318
16 85 13  319
17 1141 2 91 31
18 1815 20  2394
19 22 2055 2926
20 188  26  07
21 14  29 1
22 2218  032 31
23 2099 2885 3228
24 1214 2677 3216
25 229  2422 28 5
26 574 21 8 3053
27 576 1409 1912
28 354 1 1 3142
29 3 11 322  32 9
30 1 5 2938 31 4
31 729  5 1520
32 37 3115 3233
33 4 2 1 32 1
34 1130 2 1 30 0
35 1136 2728 3203
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate R is 13/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 17 presented below:

TABLE 17
   Index of row where 1 is located in the 0th column of the ith column group
0  37 144 161 1 9 220  96 510  89 731 808 83   65 1249 1264 1311 1377 1460 1520 1598 1707 1958 2055 2099 2154
1  20 27 165 462 54   83 742 79  1095 1110 1129 1145 1169 11 0 1254 1363 1383 1463 1718 1835 1870 1879 210  2128
2  288 362 4 3 505 638 691 745  1 1006 1083 1124 1175 1247 1275 1337 1 3 137  1506 1588 1 32 1720 1868 1980 2135
3  405 464 478 511 566 574 641 766 785 802 836 996 1128 1239 1247 1449 1491 1537 1616 1643 1668 1950 1975 2149
4  86 192 245 357 363 374 700 713 832 903 992 1174 1245 1277 1342 1369 1381 1417 1463 1712 1900 1962 2053 2118
5  101 327 378 550
6  186 723 1318 1550
7  118 277 504 1835
8  199 407 1776 1965
9  387 1253 1328 1975
10 62 144 1163 2017
11 100 475 572 2136
12 431 865 1568 2055
13 283 640 981 1172
14 220 1038 1903 2147
15 483 1318 1358 2118
16 92 961 1709 1810
17 112 403 1485 2042
18 431 1110 1130 1365
19 587 1005 1206 1588
20 704 1113 1943
21 375 1487 2100
22 1507 1950 2110
23 9 2 1913 2038
24 554 1295 1501
25 488 784 1446
26 871 1935 1964
27 54 1475  04
28 1579 1617 2074
29 1856 196  2131
30 3 0 1582 2107
31 40 1056 1809
32 1310 1353 1410
33 232 554 1939
34 168 541 1099
35 333 437 1556
36 153 622 745
37 719 931 1188
38 237 638 1 07
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 18 presented below:

TABLE 18
i  Index of row where 1 is located in the 0th column of the ith column group
0  2949 5639 7367 8468 8922 9552 11216 12483 126 2 13305 14026 15331 16463 17169 17210 18200 18744 19729 210 9 21976
   22751 23405 2 903 27283 27785 28232 30140 31378 31517 32596 33276 34715 37150 38321 39030 41119 41822
1  497 1675 2751 62 4 6502  0  9462 10174 11130 13 20 15232 1 84 1 154 19161 19289 2259  234 7 250  27490 2925
   29606 30519 30950 32038 33244 32463 34664 35613 36427 37214 39295 39721 40604 41339 4204  42956 42993
2  81 2015 3625 3922 5 12 5478 10562 12344 1525  17199 18144 18734 2 42  20680 20 92 23405 23775 26987 27051 27928
   30165 30 1 31468 31734 32911 33246 34674 35490 3 2  37198 40207 407 3 40978 41 99 42 0  42  43163
3  0 83 1 50 12379 13152 1570  18322 18837 19 30  19707 2049  20515 21 1 25442 2 973 28529 31811 33 46 33 32 34951
   36620 38616 3  39044 39113 400 9 4134  41555 41862 42402 42498 42585 42675 42993 43024 43055 430
4  0 4117 4725 7284 8569 9958 12270 13621 152 4 16 76 166 1 1 89 213  23  23 74 24076 24394 27950 30679 31287 35577
   36 92 38152 38720 3 75 39185 3 252 39340 3 775 40 87 41909 41943 424 7 42 61 42973 4 0 1 43097
5  967 2 29 3433 4645 4982 6055 92  9343 125  16491 21527 24 6  259 0 28150 28991 29257  0 1 31084 31236 31 5
   328  34483 35276 36410 37071 371 2 37300 37462 39998 40146 40154 4150  41728 42263 42446 42 10 42 00
6  20 183 4422 4776 8224 8345 9567 10020 12 21 15 94 1 523 17333 20169 20579 23118 24244 27052 27722 29664 303 0 35 72
   35 7  3 7 37033 37413 376 1 38892 39128 392  400  40772 41443 42048 4 4 424 7 47745 4 011
7  84 106 3077 11179 14909 1 393 18487 19607 22021 22690 22803 250 5 26576 27 1 27921 28711 29634 29800 35182 35277
   35908 36592 37177 371 3 372 2 385  40818 40 59 41 14 41645 41 31 41848 42076 42133 42686 42960 43081
8  11   118 190  9297 9815 11631 13409 14586 1 14 16965 2343  2 714 25 46 2676  27507 2 079 300 2 31032 31645 32997
   3441  37279 3787  38 25 39755 4109  41 30 4173  41745 41 50 42210 422 3 42 4 427 7 43073 43114
9  847 4197 18971 21073 21 32 21 04 2 372 29779 31957
10 88  2507 17001 22 5  32 23 42335 42766 42963 4306
11 10043 11 04 16616 34509 38254 39794 4034  40904 41837
12 3140 6150 19328 27432 29211 3025  34818 354 7 41 5
13 4  7561 25 0 27629 27970 36235 39071 41760 42680
14 4457 11073 22626 25705 26101 27653 37929 40444 4314
15 935  22 54 24345 2 334 2998  38991 39405 39467 42161
16 5208 6811 9103 9459 9821 17992 20176 23613 25 09
17 028 8500 18269 2 93 34977 399 7 41007 41908 43134
18 9949 18141 19765 2 691  617 41501 42181 42 13 42795
19 7088 18754 22437 24859 25  25260 2 9  40105 42107
20 1103 13160 38346
21 1001 9 145  19503
22 9430 1033  25320
23 1 076 2151  4 031
24 1655  17352 42 59
25 762 92 4 2 13
26 324  31582 40864
27 39929 41844 4 505
28 1 2 37978 42
29 1163 274 2 40918
30 29919 41247 4 965
31 5613 17  33 21
32 3162  37112 41081
33 2444 9 23 40886
34 1 47 24355 29735
35 17445 20377  34 0
36 12214 30796 42127
37 2806 10061 31670
38 18024 36307 42997
39 1786 10898 40868
40 91 12816 34474
41 14181 32766 429 3
42 14002 20589 43180
43 4615 35058 43192
44 109 10827 40754
45 17 2 7 37 41511
46 39185 42681 42708
47 2790 37933 43108
48 2024 25595 35385
49 3205 35128 36500
50 653 12 19 21362
51 158 6617 34314
52 520 42957 430 2
53 7 14 41770 43179
54 16081 227  40856
55 18163 19831 21768
56 3375 29411 43010
57 17033 22596 42767
58 11786 19137 13 11
59 52 9964 19729
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 19 presented below:

TABLE 19
i  Index of row where 1 is located in the 0th column of the ith column group
0  1606 3402 4961 6751 7132 11516 12300 12482 12592 13342 13764 1412  21576 23946 24533 25376 25667 26836 31799 34173
   35462 36153 36740 37085 37152 374 8 37658
1  4621 5007 6910 8732 9757 11508 13099 15513 16335 1 52 19512 21319 23663 25 28 27208 31333 32219 33003 33239 33447
   36200 36473 36938 37201 37283 37495 38642
2  16 1094 2020 3080 4194 5098 5631 6877 7889 8237 9 04 10067 11017 11366 13136 13354 15379 18934 20199 24522 26172
   28666 30386 3 14 36390 37015 37162
3  700 897 1708 6017 6490 7372 7825 9546 10398 16605 18561 18745 21625 22137 23693 24340 24966 25015 26995 28586 28895
   29687 33938 34520 34858 37056 38297
4  15  2010 2573 3617 4452 4958 5556 5832 6481 8227 9924 10836 14954 15594 16623 18065 19249 22394 22677 23408 23731
   24076 24776 27007 28222 30343 38371
5  3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 15536 20218 21921 28599 29445 29758 29968 31014 32027 33 5
   34378 35867 36323 36728 36870 38335 38623
6  1264 4254 6936 9165 9486 9950 10861 11653 13697 13961 15164 15665 18444 19470 20313 2118  24371 26431 26999 28086
   28251 29261 31981 34015 35850 36129 37186
7  111 1307 1628 2041 2524 5358 7988 8191 10322 11905 12919 14127 15515 15711 17061 19024 21195 22902 23727 24401
   24608 25111 25228 27338 35398 37794 38196
8  961 3035 7174 7948 13355 13607 14971 18189 18339 18665 18875 19142 20615 21136 21309 21758 23366 24745 25849 25962
   27583 30006 31118 32106 36469 36583 37920
9  2990 3549 4273 4808 5707 6021 6509 7456 8240 10044 12262 12660 13085 14750 15680 16049 21587 23997 25803 28343
   28693 34393 34860 35490 36021 37737 38296
10 955 4323 5145 6885 8123 9730 11840 12216 19194 20313 23056 24248 24830 25268 26617 26801 28557 29753 30745 31450
   31973 32839 33025 33296 35710 37366 3750
11 264 605 4181 4483 5156 7238 8863 10939 11251 12964 16254 17511 20017 22395 22818 23261 23422 24064 26329 27723
   28186 30434 31956 33971 34372 36764 38123
12 520 25 2 2794 3528 3860 4402 5 76 6963 8655 9018 9783 11933 16336 17193 17320 19035 20 06 23579 23769 24123 24966
   27866 32457 34011 34499 36620 37526
13 10106 10637 10906 34242
14 1856 15100 19378 21848
15 943 11191 27806 29411
16 4575 6359 13629 19383
17 4476 4953 18782 24313
18 5441  381 21840 35943
19 9638 9763 12546 30120
20 9587 10626 11047 25700
21 4088 15298 28768 35047
22 2332  363 8782 28863
23 4625 4933 28298 30289
24 3541 4918 18257 31746
25 1221 25233 2 757 34892
26 8150 1 677 27934 30021
27 8500 2501  33043 38070
28 7374 10207 16189 35811
29 611 18480 20064 382 1
30 25416 27352 36089 384 9
31 16 7 17614 2583  32776
32 4118 12481 21912 37945
33 5573 13222 23619 31271
34 18271 2 251 27182 3 587
35 14690 26430 26799 34355
36 13688 16040 20716 3455
37 2740 14957 23436 32540
38 3491 14365 14681 36858
39 4796 62 8 25203 27854
40 1731 12816 17344 26025
41 19182 21662 23742 27872
42 6502 13641 17509 34713
43 12246 12372 16746 27452
44 1589 21528 30621 34003
45 12328 20515 30651 31432
46 3415 22656 23427 36395
47 32 5209 25958 31085
48 19 3690 19648 37778
49 9528 13581 26965 36447
50 2147 26249 26968 28776
51 15698 18209 30683
52 1132 19888 34111
53 4608 25513 38874
54 475 1729 34100
55 7348 32277 38587
56 182 1 473 33082
57 3865 9678 212 5
58 4447 20151 27618
59 6335 14371 38711
60 704 9695 28858
61 4856 9757 30546
62 1993 19361 30732
63 756 28000 29138
64 3821 24076 31813
65 4611 12326 32291
66 628 21515 34995
67 1246 13294 300 8
68 6466 33233 35865
69 14484 23274 38150
70 21269 36411 37450
71 23129 26195 37653
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 20 or 21 presented below:

TABLE 20
i  Index of row where 1 is located in the 0th column of the ith column group
0  13 127 927 930 1 06 2348 3361 37 4 5194 6327 7843 8081 8615 12199 13947 15317 15774 16289 16687 17122 20468 21057
   21853 22414 23829 23885 25452 28072 28699 28947 30289 31672 32470
1  36 53 60 86 93 407 3 75 4478 5884 6578 75 9 7613 7 6 9573 11010 11183 11233 13750 171 2 17860 20181 23974 24195
   25089 25787 25892 26121 30880 32989 33383 33626 34153 34520
2  27 875 2693 3435 3682 6195 6227 6711 7 29 8005 9081 11052 11190 11443 14 2 17431 17756 1799  18254 18632 22234
   22880 235 2 23647 27092 29035 29620 3033  33492 33906 33960 34337 34474
3  10 722 1241 3558 5490 550  6420 7128 12386 12847 12942 15305 1559 2 16799 18033 1 134 20713 20870 215 9 2638 0 27538
   27577 27971 29744 32344 32347  2673 32892 3301  33674 33811 34253 34511
4  6 24 72 2552 3171 5179 11519 12484 13096 13282 15226 18193 19995 25166 25303 25693 26821 2919  30666 31952 33137
   33187 33190 33319 336 3 33950 34062 34255 34292 34365 34433 34443 34527
5  1 12 26 29 85 153  3870 6763 7533 7630 8022 8857 11667 11919 14987 16133 20999 21830 23522 2416  27671 284 1 30618
   31556 31894 33436 33543 34146 34197 34313 34437 34480 34550
6  13 44 2482 5068 8153 13233 13728 14548 17278 20027 21273 22112 22376 24799 29175
7  26 50 8325 8 91 12816 15672 1593  24049 30372 31245 33194 33238 3393  34093 34547
8  1412 6334 7945 8866 10886 14521 17224 23693 25160 29267 313 7 31893 32346 33195 33687
9  27 47 14505 14786 18416 19963 23250 23475 27275 27921 2809  33985 34371 34374 34512
10 16 31 4924 7028 10240 12380 13479 16405 20197 27989 2808 4 32440 3399  34090 34435
11 17 57 95 6786 7427 7548 10452 13714 25632 30647 33054 34195 34237 34304 34447
12 4 62 331 10220 10518 10575 18401 19286 28718 30521 30968 31329 31848 32614 34343
13 42 79 4682 4747 7335 11487 17405 18089 19470 22457 33433 34373 34471 34519 34540
14 27 65 4911 10752 14803 24122 24531 25322 29130 30081 31280 32050 32693 34435 34508
15 24 29 2107 2152 5271 11032 14001 14902 21705 2312  31276 33946 34372 34380 34469
16 16 62 72 7470 14839 15299 15894 1771  18068 24959 25024 33343 34186 34 98 34429
17 37 56 70 2089 10016 11316 14652 15665 17202 19804 19847 30498 33938 34126 34391
18 68 963 2099 9596 17606 19249 21839 27437 29901 30714 33060 33456 34347 34498 34527
19 6 69 1845 2504 7189 8603 10379 11421 13742 15757 16857 20642 28039 32833 34270
20 2235 15032 31823
21 4737 33978 34504
22 2 20263 30373
23 923 18929 25743
24 4587 22945 28380
25 22094 26147 34544
26 5177 20758 26476
27 8938 17291 27352
28 5286 24717 29331
29 71 16442 32683
30 81 22810 28015
31 14112 14419 29708
32 4156 7522 23358
33 12850 20777 28294
34 14 92 31178 342 8
35 3447 12356 21997
36 6098 15443 33447
37 5947 11648 21719
38 72 8695 18421
39 2173 18978 27232
40 13656 18222 19869
41 49 24684 33849
42 84 13870 18354
43 54 10089 10516
44 8035 18741 23775
45 7553 13539 25652
46 9116 26724 27525
47 22960 24382 2618
48 17384 24749 26726
49 12197 18965 32473
50 95 23126 26909
51 19327 31338 34320
52 9843 34130 34 81
53 4031 9940 22329
54 58 3179  34468
55 103 17411 25220
56 26 4338 24625
57 9758 34395 34531
58 2186 17077 27646
59 9156 194 2 34059
60 6 59 29352
61 16316 29453 34128
62 1 244 32865 34517
63 918 22159 29265
64 13612 19465 20671
65 1 8261 8849
66 11214 28864 32696
67 11513 27595 34479
68 11895 21430 34524
69 82 5535 10552
70 66 15799 2 966
71 20555 21816 32855
72 3772 27923 33492
73 12837 15856 21575
74 2 16865 34413
75 2682 2702 21630
76 10 22173 34016
77 9740 23216 33800
78 61 33792 33839
79 3961 29314 33446
80 11337 16620 20008
81 184 1 25285 34267
82 46 117  394
83 122 1 25671 34505
indicates data missing or illegible when filed

TABLE 21
i  Index of row where 1 is located in the 0th column of the ith column group
0  7 15 26 69 1439 3712 5756 5792 5911 8456 10579 19462 19782 2170  2 214 25142 2 040 30206 30475 31211 31427 3210
   32989 33082 33502 3411  34241 34288 34292 34318 34373 34390 34465
1  83 1159 2271 6500 6807 7823 10344 10700 13367 141 2 142 2 14352 15015 17 301 1 52 20811 24974 25795 27868 280 1
   33077 33204 33262 33350 33516 33677 33680 33930 34090 34250 34290 34377 34398
2  25 2281 2995 3321 6006 7482 8428 11489 11601 14011 17409 26210 29945 3067  31101 31355 31421 31543 31697 32056 3221
   33282 33453 33487 33696 34044 34107 34213 34247 34261 34276 34467 34495
3  0 43  87 2530 4485 4595 9951 11212 12270 12344 15566 21335 24699 26580 28518 28564 2 12 29 21 30418 31467 31871
   32 13 3259  33187 3 402 33706 338 8 339 2 33977 34084 34283 34440 34473
4  81 3344 5540 7711 13308 15400 15885 18265 18632 2220  23657 27736 29158 29701 29 45  0409 30654 30855 31420 316 4
   32519 32901 33267 33444 33525 33712 33878 34031 34172 34432 34496 34502 34541
5  42 50 66 2501 4706 6715 6 70  637 9999 14555 22776 26479 27442 27984 285 4 295 7 31309 317 3 31907 31927 31934 32313
   32369 32 0 33364 33434 33553 33654 33725 33889 3396 2 344 7 344 2
6  6534 7122 8723 13137 13183 15818 18 07 19324 20017 26389 29326 31464 32678 33668 34217
7  50 113 2119 5038 5581 6397 6550 10987 22308 25141 25943 29299 30186 33240 33399
8  7262 8787 9246 10032 10505 13090 14587 14790 16374 19946 21129 25726 31033 33660 33675
9  5004 5087 5291 7949 9477 11 45 1269  14585 15239 17486 18100 18259 21409 2178  24280
10 28 82 3939 5007 6 2 10312 12485 14384 21570 25512 26612 2 854 30371 31114 32
11 437 3055 9100 9517 12369 19030 19950 21328 24196 242 6 2592  28458 30013 32181 33560
12 1  35 0 4832 705  8919 21149 24256 26543 27266 30747 31 9 32671 33089 33571 34296
13 2678 4569 4667 6551 7639 10057 24276 24563 25818 26 2 27879 28 02  29444 29873 34017
14 72 77 2874 9092 10041 13669 20676 20778 25566 28470 28888 3033  31772 32143 33939
15 296 2196 7309 11901 14025 15733 16768 2 87 25489 30936 31533 33749 34331 34431 34507
16 6 8144 12490 13275 14140 18706 20251 2 44 21441 21938 23703 34190 34444 34463 34495
17 5108 14499 15734 19222 24695 25667 28359 28432 30411 30720 34161 34386 34465 34511 34522
18 61 89 3042 5524 12128 22 05 22700 22919 24454 30526 33437 34114 34188 344 0 34502
19 11 83 4668 4856 6361 11633 15342 163 3 16958 26613 29136 30917 32559 34346 34504
20 3185 9728 25062
21 1643 5531 21573
22 2285 6088 24083
23 78 14678 19119
24 49 13705 33535
25 21192 32280 32781
26 10753 21469 22084
27 10082 11 50 13889
28 7861 25107 29167
29 14 51 34171 34430
30 706 894 8316
31 29693 30445 32281
32 10202 30964 34448
33 15815 32453 34463
34 4102 21608 24740
35 4472 29399 31435
36 1162 7118 23226
37 4791 33548 34096
38 1084 34099 34418
39 1765 20745 33714
40 1302 21300 33655
41 33 8736 16646
42 53 18671 19089
43 21 572 2028
44 3339 11506 16745
45 285 6111 12643
46 27 10336 11586
47 21046 32728 34538
48 22215 24195 34026
49 19975 26938 29374
50 16473 2 777 34212
51 20 292 0 327 4
52 35 31645 32837
53 26132 34410 34495
54 12446 2 649 26851
55 6796 10992 31061
56 0 46 8420
57 10 636 22885
58 7183 16342 1 305
59 1 56 4 28258
60 6071 18675 34489
61 1678  25023 33323
62 3573 5081 10925
63 5067 31761 34415
64 3735 33534 34522
65 85 32 29 34518
66 6555 23368 34559
67 22083 29335 29390
68 67  21110 34316
69 120 4192 11123
70 3313 4144 20824
71 277 3 28550 31034
72 6597 8164 34427
73 1 00  23474 32460
74 94 6342 12656
75 17  1962 34535
76 15091 24955 2 8545
77 15 3213 28298
78 265 2  0236 3 4537
79 16 32 20334 24628
80 4841 20669 26509
81 18055 2 700 34534
82 23576 31496 34492
83 10699 13826  4440
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 22 presented below:

TABLE 22
i  Index of row where 1 is located in the 0th column of the ith column group
0  2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 11521 12083 16610 18361 20321 24601 27420 28206 29788
1  2739 8244 8891 9157 12624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 25540 27478 27678 28053
2  1727 2268 6246 7815 9010 9556 10134 10472 11389 14599 15719 16204 17342 17666 18850 22058 25579 25860 29207
3  28 1346 3721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 19357 19473 19891 20381 23911 29683
4  869 2450 4386 5316 6160 7107 10362 11132 11271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804
5  508 4292 58 31 8559 10044 10412 11283 14810 15888 17243 17538 19903 20528 22090 22652 27235 27384 28208 28485
6  389 2248 5840 6043 7000 9054 11075 117 0 12217 12565 13587 15403 19422 19528 21493 2 142 27777 28566 287 2
7  1015 2002 5764 6777 9346 9629 11039 11153 12 0 130  13990 16841 17702 20021 24106 26300 29332 30081 30196
8  1480 3084 3467 4401 4798 5187 7851 11368 12323 14325 14546 16360 17158 1 10 21333 25612 26556 2 06 27005
9  6925 8876 12 92 14529 15253 15437 19226 19950 20321 23021 23651 24393 246  26668 27205 28269 28529 29041 29292
10 2547 3404 3538 4666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 19717 22150 24941 27908 29018
11 888 1581 2311 5511 7218 9107 10454 12252 13662 15714 15894 17025 18671 24304 25316 25556 28489 2 77 29212
12 1047 14 4 1718 4645 5030 6811 7868 8146 10611 15767 17682 1 91 22614 23 21 23763  478 26491 29088 29757
13 59 1781 190  3814 4121 8 044 8906 9175 11156 14841 15789 16033 16755 17292 18550 19310 22505 29567 29850
14 1952 3057 4399 9476 10171 10769 11 5 11569 15002 19501 20621 22642 23452 24360 25109 25290 2 828 28505 29122
15 2895 3070 3437 47 4 4905  670 9244 11845 13352 1357  13975 14600 15 71 17996 19672 20079 2 579 25327 2795
16 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 18413 190 8 22985 24257 26202 26596 27899
17 1361 2195 4146  708 7158 7538 9138 9998 14 2 1 359 1 076 1 925 21401 21573 2250  24146 24247 2777  29 12
18 5229 6235 7134 7655 9139 13527 1540  1605 8 1670  1 320 19909 20901 222 8 22437 23654 25131 27550 28247 29903
19 697 2035 4887  275 6909 9166 11805 15338 16381 18403 20425 206  21 47 24 590 2 171 26726 2 48 29224 29412
20 5379 17329 22659 2 062
21 11 14 14759 22329 22936
22 2423 2811 10296 12727
23 8460 1526  16769 17290
24 14191 146  29 6 301 7
25 7103 100 9 20111 22 50
26 4285 15413 2644  290
27 548 2137 9189 1092
28 45 1 7 77 23382 2 949
29 3942 17248 19486 27922
30 8668 10230 16922 26678
31 6158 9980 13788 28198
32 12422 16076 24206 29887
33 8778 10649 18747 22111
34 21029 22677 27150 28980
35 7918 15423 27672 27803
36 5927 18086 23525
37 3397 15058 30224
38 24016 25880 26268
39 1096 4775 7912
40 3259 17301 20802
41 129 8396 15132
42 17825 28119 28676
43 2343 8382 28840
44 3907 18374 20939
45 1132 1290 8786
46 1481 4710 28846
47 2185 3705 26834
48 5496 15 1 21854
49 12697 13407 22178
50 12788 21227 22894
51 629 2854 6232
52 2289 18227 27458
53 7593 21935 23001
54 3836 7081 12282
55 7925 18 440 23135
56 497 6342 9717
57 11199 22046 30067
58 12572 28045 28990
59 1240 2023 10933
60 19566 20 29 25186
61 6442 13303 2 13
62 4765 10572 161 0
63 552 19 01 242 6
64 67 2 18480 21383
65 11267 12288 15758
66 771 5652 15531
67 16131 20047 25649
68 13227 23035 24450
69 4839 13467 27488
70 2 52 4 77 22993
71 2504 28116 29524
72 12518 17374 24267
73 1222 11859 27922
74 9660 17286 18261
75 232 11296 29978
76 9750 11165 16295
77 4 94 9505 23622
78 10861 11980 14110
79 2128 15883 22836
80 274 17243 21989
81 108 6 13202 22 17
82 11159 16111 21608
83 3719 18787 22100
84 1756 2020 23901
85 20913 29473 30103
86 2729 15 1 26976
87 4410 8217 12963
88 5395 24564 28235
89 3859 17  23051
90 5733 26005 29797
91 1935 3492 29773
92 11903 21380 29914
93 6091 10469 29997
94 2895 8930 15594
95 1827 10028 20 70
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 23 presented below:

TABLE 23
i   Index of row where 1 is located in the 0th column of the ith column group
0   113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339
1   271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910
2   73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600
3   1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177
4   1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913
5   28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680
6   0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863
7   29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395
8   55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872
9   1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915
10  7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 2 293 25403
11  48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802
12  12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838
13  3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880
14  21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814
15  18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906
16  4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24882 24613 25689 25855 25883
17  0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19 5 20253 21996 24136 24890 25758 25784 25807
18  34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644
19  1595 6216 22850 25439
20  1562 15172 19517 22362
21  7508 12879 24324 24496
22  6298 15819 16757 18721
23  11173 15175 19966 21195
24  59 13505 16941 23793
25  2267 4830 12023 20587
26  8827 9278 13072 16664
27  14419 17463 23398 25348
28  6112 16534 20423 22698
29  493 8914 21103 24799
30  6896 12761 13206 25873
31  2 1380 12322 21701
32  11600 21306 25753 25790
33  8421 13076 14271 15401
33  8421 13076 14271 15401
34  9630 14112 19017 20955
35  212 13932 21781 25824
36  5961 9110 16654 19636
37  58 5434 9936 12770
38  6575 11433 19798
39  2731 7338 20926
40  14253 18463 25404
41  21791 24805 25869
42  2 11646 15850
43  6075 8586 23819
44  18435 22093 24851
45  2103 2368 11704
46  10925 17402 18232
47  9062 25061 25674
48  18497 20853 23404
49  18606 19364 19551
50  7 1022 25543
51  6744 15481 25868
52  9081 17305 25164
53  8 23701 25883
54  9680 19955 22848
55  56 4564 19121
56  5595 15086 25892
57  3174 17127 23183
58  19397 19817 20275
59  12561 24571 25825
60  7111 9889 25865
61  19104 20189 21851
62  549 9686 25548
63  6586 20325 25906
64  3224 20710 21637
65  641 15215 25754
66  13484 23729 25818
67  2043 7493 24246
68  16860 25230 25768
69  22047 24200 24902
70  9391 18040 19499
71  7855 24336 25069
72  23834 25570 25852
73  1977 8800 25756
74  6671 21772 25859
75  3279 6710 24444
76  24099 25117 25820
77  5553 12306 25915
78  48 11107 23907
79  10832 11974 25773
80  2223 17905 25484
81  16782 17135 20446
82  475 2861 3457
83  16218 22449 24362
84  11716 22200 25897
85  8315 15009 22633
86  13 20480 25852
87  12352 18658 25687
88  3681 14794 23703
89  30 24531 25846
90  4103 22077 24107
91  23837 25622 25812
92  3627 13387 25839
93  908 5367 19388
94  0 6894 25795
95  20322 23546 25181
96  8178 25260 25437
97  2449 13244 22565
98  31 18928 22741
99  1312 5134 14838
100 6085 13937 24220
101 66 14633 25670
102 47 22512 25472
103 8867 24704 25279
104 6742 21623 22745
105 147 9948 24178
106 8522 24261 24307
107 19202 22406 24609
indicates data missing or illegible when filed

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 10/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 24 or 25 presented below:

TABLE 24
i   Index of row where 1 is located in the 0th column of the ith column group
0   979 1423 4166 4609 6341 8258 10334 10548 14098 14514 17051 17333 17653 17830 7990
1   2559 4025 6344 6510 9167 9728 11312 14856 17104 17721 18600 18791 19079 19697 19840
2   3243 6894 7950 10539 12042 13233 13938 14752 15449 16727 17025 18297 18796 19400 21577
3   3272 3574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 17309 19415 19845
4   155 4598 10201 10975 11086 11296 12715 15364 15978 16395 17542 18164 18451 18612 20617
5   1128 1999 3926 4069 5558 6085 6337 8386 10693 12450 15438 16223 16370 17308 18634
6   2408 2929 3630 4357 5852 7329 8536 8695 10603 11003 14304 14937 15767 18402 21502
7   199 3066 6446 6849 8973 9536 10452 12857 13675 15913 16717 17654 19802 20115 21579
8   312 870 2095 2386 5517 6196 6757 7311 7368 13046 15364 18576 20349 21424 21587
9   985 1591 3248 3509 3706 3847 6174 6276 7864 9033 13618 15675 16446 18355 18843
10  975 3774 4083 5825 6166 7218 7633 9657 10103 1 052 14240 17320 18126 19544 20208
11  1795 2005 2544 3418 6148 8051 9068 9725 10676 10752 11512 15171 17523 20481 21059
12  167 315 1824 2325 2640 2868 6070 6597 7016 8109 9815 11608 16142 17912 19625
13  1298 1896 3039 4303 4690 8787 12241 13600 14478 15492 16602 17115 17913 19466 20597
14  568 3695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 19218 21506
15  228 1889 1967 2299 3011 5074 7044 7596 7689 9534 10244 10697 11691 17902 21410
16  1330 1579 1739 2234 3701 3865 5713 6677 7263 11172 12143 12765 17121 20011 21436
17  303 1668 2501 4925 5778 5985 9635 10140 10820 11779 11849 12058 15650 20426 20527
18  698 2484 3071 3219 4054 4125 5663 5939 6928 7086 8054 12173 16280 17945 19302
19  232 1619 3040 4901 7438 8135 9117 9233 10131 13321 17347 17436 18193 18586 19929
20  12 3721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 16264 18883
21  482 915 1548 1637 6 87 9338 10163 11768 11970 15524 15695 17386 18787 19210 19340
22  1291 2500 4109 4511 5099 5194 10014 13165 13256 13972 15409 16113 16214 18584 20998
23  1761 4778 7444 7740 8129 8341 8931 9136 9207 10003 10678 13959 17673 18194 20990
24  3060 3522 5361 5692 6833 8342 8792 11023 11211 11548 11914 13987 15442 15541 19707
25  1322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 16680 16970 21321
26  6785 11960 21455
27  1223 15672 19550
28  5976 11335 20385
29  2818 9387 15317
30  2763 3554 18102
31  5230 11489 18997
32  5809 15779 20674
33  2620 17838 18533
34  3025 9342 9931
35  3728 5337 12142
36  2520 6666 9164
37  12892 15307 20912
38  10736 12393 16539
39  1075 2407 12853
40  4921 5411 18206
41  5955 15647 16838
42  6384 10336 19266
43  429 10421 17266
44  4880 10431 12208
45  2910 11895 12442
46  7366 18362 18772
47  4341 7903 14994
48  4564 6714 7378
49  4639 8652 18871
50  15787 18048 20246
51  3241 11079 13640
52  1559 2936 15881
53  2737 6349 10881
54  10394 16107 17073
55  8207 9043 12874
56  7805 16058 17905
57  11189 15767 17764
58  5823 12923 14316
59  11080 20390 20924
60  568 8263 17411
61  1845 3557 6562
62  2890 10936 14756
63  9031 14220 21517
64  3529 12955 15902
65  413 6750 8735
66  6784 12092 16421
67  12019 13794 15308
68  12588 15378 17676
69  8067 14589 19304
70  1244 5877 6085
71  15897 19349 19993
72  1426 2394 12264
73  3456 8931 12075
74  13342 15273 20351
75  9138 13352 20798
76  7031 7626 14081
77  4280 4507 15617
78  4170 10569 14335
79  3839 7514 16578
80  4688 12815 18782
81  4861 7858 9435
82  605 5445 12912
83  2280 4734 7311
84  6668 8128 12638
85  3733 10621 19534
86  13933 18316 19341
87  1786 3037 21566
88  2202 13239 16432
89  4882 5808 9300
90  4580 8484 16754
91  14630 17502 18269
92  6889 11119 12447
93  8162 9078 16330
94  6538 17851 18100
95  17763 19793 20816
96  2183 11907 17567
97  6640 14428 15175
98  877 12035 14081
99  1336 6468 12328
100 5948 9146 12003
101 3782 5699 12445
102 1770 7946 8244
103 7384 12639 14989
104 1469 11586 20959
105 7943 10450 15907
106 5005 8153 10035
107 17750 18826 21513
108 4725 8041 10112
109 3837 16266 17376
110 11340 17361 17512
111 1269 4611 4774
112 2322 10813 16157
113 16752 16843 18959
114 70 4325 18753
115 3165 8153 15384
116 160 8045 16823
117 14112 16724 16792
118 4291 7667 18176
119 5943 19879 20721
indicates data missing or illegible when filed

TABLE 25
i   Index of row where 1 is located in the 0th column of the ith column group
0   316 1271 3692 9495 12147 12849 14928 16671 16938 17864 19108 20502 21097 21115
1   2341 2559 2643 2816 2865 5137 5331 7000 7523 8023 10439 10797 13208 15041
2   5556 6858 7677 10162 10207 11349 12321 12398 14787 15743 15859 15952 19313 20879
3   349 573 910 2702 3654 6214 9246 9353 10638 11772 14447 14953 16620 19888
4   204 1390 2887 3855 6230 6533 7443 7876 9299 10291 10896 13960 18287 20086
5   541 2429 2838 7144 8523 8637 10490 10585 11074 12074 15762 16812 17900 18548
6   733 1659 3838 5323 5805 7882 9429 10682 13697 16909 18846 19587 19592 20904
7   1134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 17417 18960 20303
8   734 1001 1283 4959 10016 10176 10973 11579 12051 15550 15915 19022 19430 20121
9   745 4057 5855 9885 10594 10989 13156 13219 13351 13631 13685 14577 17713 20386
10  968 1446 2130 2502 3092 3787 5323 8104 8418 9998 11681 13972 17747 17929
11  3020 3857 5275 5786 6319 8608 11943 14062 17144 17752 18001 18453 19311 21414
12  709 747 1038 2181 5320 8292 10584 10859 13964 15009 15277 16953 20675 21509
13  1663 3247 5003 5760 7186 7360 10346 14211 14717 14792 15155 16128 17355 17970
14  516 578 1914 6147 9419 11148 11434 13289 13325 13332 19106 19257 20962 21556
15  5009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110 18249 20616 20759
16  457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664 18777 20152 20848
17  33 2877 5334 6851 7907 8654 10688 15401 16123 17942 17969 18747 18931 20224
18  87 897 7636 8663 11425 12288 12672 14199 16435 17615 17950 18953 19667 20281
19  1042 1832 2545 2719 2947 3672 3700 6249 6398 6833 11114 14283 17694 20477
20  326 488 2662 2880 3009 5357 6587 8882 11604 14374 18781 19051 19057 20508
21  854 1294 2436 2852 4903 6466 7761 9072 9564 10321 13638 15658 16946 19119
22  194 899 1711 2408 2786 5391 7108 8079 8716 11453 17303 19484 20989 21389
23  1631 3121 3994 5005 7810 8850 10315 10589 13407 17162 18624 18758 19311 20301
24  736 2424 4792 5600 6370 10061 16053 16775 18600
25  1254 8163 8876 9157 12141 14587 16545 17175 18191
26  388 6641 8974 10607 10716 14477 16825 17191 18400
27  5578 6082 6824 7360 7745 8655 11402 11665 12428
28  3603 8729 13463 14698 15210 19112 19550 20727 21052
29  48 1732 3805 5158 15442 16909 19854 21071 21579
30  11707 14014 21531
31  1542 4133 4925
32  10083 13505 21198
33  14300 15765 16752
34  778 1237 11215
35  1325 3199 14534
36  2007 14510 2599
37  1996 5881 16429
38  5111 15018 15980
39  4989 10681 12810
40  3763 10715 16515
41  2259 10080 15642
42  9032 11319 21305
43  3915 15213 20884
44  11150 15022 20201
45  1147 6749 19625
46  12139 12939 18870
47  3840 4634 10244
48  1018 10231 17720
49  2708 13056 13393
50  5781 11588 18888
51  1345 2036 5252
52  5908 8143 15141
53  1804 13693 18640
54  10433 13965 16950
55  9568 10122 15945
56  547 6722 14015
57  321 12844 14095
58  2632 10513 14936
59  6369 11995 20321
60  9920 19136 21529
61  1990 2726 10183
62  5763 12118 15467
63  503 10006 19564
64  9839 11942 194752
65  11205 13552 15389
66  8841 13797 19697
67  124 6053 18224
68  6477 14406 21146
69  1224 8027 16011
70  3046 4422 17717
71  739 12308 17760
72  4014 4130 7835
73  2266 5652 11981
74  2711 7970 18317
75  2196 15229 17217
76  8636 13302 16764
77  5612 15010 16657
78  615 1249 4639
79  3821 12073 18506
80  1066 16522 21536
81  11307 18363 19740
82  3240 8560 10391
83  3124 11424 20779
84  1604 8861 17394
85  2083 7400 8093
86  3218 7454 9155
87  9855 15998 20533
88  316 2850 20652
89  5583 9768 10333
90  7147 7713 18339
91  12607 17428 21418
92  14216 16954 18164
93  8477 15970 18488
94  1632 8032 9751
95  4573 9080 13507
96  11747 12441 13876
97  1183 15605 16675
98  4406 10264 17109
99  5495 7882 12150
100 1010 3763 5065
101 9828 18054 21599
102 6342 7353 15358
103 6362 9462 19999
104 7184 13693 17622
105 4343 4654 10995
106 7099 8466 18520
107 11505 14395 15138
108 6779 16691 18726
109 7146 12644 20196
110 5865 16728 19634
111 4657 8714 21246
112 4580 5279 18750
113 3767 6620 18905
114 9209 13093 17575
115 12486 15875 19791
116 8046 14636 17491
117 2120 4643 13206
118 6186 9675 12601
119 784 5770 21585

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate R is 12/15, and M is 360, the indexes of the rows where 1 is located in the 0^th column of the i^th column group of the information word submatrix 210 are as shown in Table 26 presented below:

TABLE 26
i   Index of row where 1 is located in the 0th column of the ith column group
0   584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632 8940 9725
1   221 445 590 3779 3835 6939 7743 8280 8448 8491 9367 10042 11242 12917
2   4662 4837 4900 5029 6449 6687 6751 8684 9936 11681 11811 11886 12089 12909
3   2418 3018 3647 4210 4473 7447 7502 9490 10067 11092 11139 11256 12201 12383
4   2591 2947 3349 3406 4417 4519 5176 6672 8498 8863 9201 11294 11376 12184
5   27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310 10798 12439
6   1765 1897 2923 3584 3901 4048 6963 7054 7132 9165 10184 10824 11278 12669
7   2183 3740 4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118 12762
8   73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406 10120 10507 10691
9   240 732 1215 2185 2788 2830 3499 3881 4197 4991 6425 7061 9756 10491
10  831 1568 1828 3424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458
11  2024 2970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873 11787 11837
12  1049 1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 983 11744 11937
13  1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243
14  978 2120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639
15  2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 12162 12941
16  1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 11038 12340 12440
17  289 384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425 11745 12 30
18  155 354 1090 1330 2002 2236 3559 3705 4922 5958 6576 8564 9972 12760
19  303 876 2059 2142 5244 5330 6644 7576 8614 9598 10410 10718 11033 12957
20  3449 3617 4408 4602 4727 6182 8835 8928 9372 9644 10237 10747 11655 12747
21  811 2565 2820 8677 8974 9632 11069 11548 11839 12107 12411 12695 12812 12890
22  972 4123 4943 6385 6449 7339 7477 8379 9177 9359 10074 11709 12552 12831
23  842 973 1541 2262 2905 5276 6758 7099 7894 8128 8325 8663 8375 10050
24  474 791 968 3902 4924 4965 5085 5908 6109 6329 7931 9038 9401 10568
25  1397 4461 4658 5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692
26  1334 7571 12881
27  1393 1447 7972
28  633 1257 10597
29  4843 5102 11056
30  3294 8015 10513
31  1108 10374 10546
32  5353 7824 10111
33  3398 7674 8569
34  7719 9478 10503
35  2997 9418 9581
36  5777 6519 11229
37  1966 5214 9899
38  6 4088 5827
39  836 9248 9612
40  483 7229 7548
41  7865 8289 9804
42  2915 11098 11900
43  6180 7096 9481
44  1431 6786 8924
45  748 6757 8625
46  3312 4475 7204
47  1852 8958 11020
48  1915 2903 4006
49  6776 10886 12531
50  2594 9998 12742
51  159 2002 12079
52  853 3281 3762
53  5201 5798 6413
54  3882 6062 12047
55  4133 6775 9657
56  228 6874 11183
57  7433 10728 10864
58  7735 8073 12734
59  2844 4621 11779
60  3909 7103 12804
61  6002 9704 11060
62  5864 6856 7681
63  3652 5869 7605
64  2546 2657 4461
65  2423 4203 9111
66  244 1855 4691
67  1106 2178 6371
68  391 1617 10126
69  250 9259 10603
70  3435 4614 6924
71  1742 8045 9529
72  7667 8875 11451
73  4023 6108 6911
74  8621 10184 11650
75  6726 10861 12348
76  3228 6302 7388
77  1 1137 5358
78  381 2424 8537
79  3256 7508 10044
80  1980 2219 4569
81  2468 5699 10319
82  2803 3314 12808
83  8578 9642 11533
84  829 4585 7923
85  59 329 5575
86  1067 5709 6867
87  1175 4744 12219
88  109 2518 6756
89  2105 10626 11153
90  5192 10696 10749
91  6260 7641 8233
92  2998 3094 11214
93  3398 6466 11494
94  6574 10448 12160
95  2734 10755 12780
96  1028 7958 10825
97  8545 8602 10793
98  392 3398 11417
99  6639 9291 12571
100 1067 7919 8934
101 1064 2848 12753
102 6076 8656 12690
103 5504 6193 10171
104 1951 7156 7356
105 4389 4780 7889
106 526 4804 9141
107 1238 3648 10464
108 2587 5624 12557
109 5560 5903 11963
110 1134 2570 3297
111 10041 11583 12157
112 1263 9585 12912
113 3744 7898 10646
114 45 9074 10315
115 1051 6188 10038
116 2242 8394 12712
117 3598 9025 12651
118 2295 3540 5610
119 1914 4378 12423
120 1766 3635 12759
121 5177 9586 11143
122 943 3590 11649
123 4864 6905 10454
124 5852 6042 10421
125 6095 8285 12349
126 2070 7171 8563
127 718 12234 12716
128 512 10 67 11353
129 3629 6485 7040
130 2880 8865 11466
131 4490 10220 11796
132 5440 8819 9103
133 5262 7543 12411
134 516 7779 10940
135 2515 5843 9202
136 4684 5994 10586
137 573 2270 3324
138 7870 8317 10322
139 6856 7638 12909
140 1583 7669 10781
141 8141 9085 12555
142 3903 5485 9992
143 4467 11998 12904
indicates data missing or illegible when filed

According to an exemplary embodiment, even when the order of numbers, i.e., indexes, in a sequence corresponding to the i^th column group of the parity check matrix 200 as shown in the above-described Tables 4 to 26 is changed, the changed parity check matrix is a parity check matrix used for the same LDPC code. Therefore, a case in which the order of numbers in the sequence corresponding to the i^th column group in Tables 4 to 26 is changed is covered by the inventive concept.

According to an exemplary embodiment, even when one sequence corresponding to one column group is changed and another sequence corresponding to another column group are changed to each other in Tables 4 to 26, cycle characteristics on a graph of the LDPC code and algebraic characteristics such as degree distribution are not changed. Therefore, a case in which the arrangement order of the sequences shown in Tables 4 to 26 is changed is also covered by the inventive concept.

In addition, even when a multiple of Q_ldpc is equally added to all numbers, i.e., indexes, corresponding to a certain column group in Tables 4 to 26, the cycle characteristics on the graph of the LDPC code or the algebraic characteristics such as degree distribution are not changed. Therefore, a result of equally adding a multiple of Q_ldpc to the sequences shown in Tables 4 to 26 is also covered by the inventive concept. However, it should be noted that, when the resulting value obtained by adding a multiple of Q_ldpc to a given sequence is greater than or equal to (N_ldpc−K_ldpc), a value obtained by applying a modulo operation for (N_ldpc−K_ldpc) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^th column of the i^th column group of the information word submatrix 210 are defined as shown in Tables 4 to 26, positions of rows where 1 exists in another column of each column group may be defined since the positions of the rows where 1 exists in the 0^th column are cyclic-shifted by Q_ldpc in the next column.

For example, in the case of Table 4, in the 0^th column of the 0^th column group of the information word submatrix 210, 1 exists in the 245^th row, 449^th row, 491^st row, . . . .

In this case, since Q_ldpc=(N_ldpc−K_ldpc)/M=(16200−5400)/360=30, the indexes of the rows where 1 is located in the 1^st column of the 0^th column group may be 275(=245+30), 479(=449+30), 521(=491+30), . . . , and the indexes of the rows where 1 is located in the 2^nd column of the 0^th column group may be 305(=275+30), 509(=479+30), 554=521+30).

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2 may be defined as follows:

The parity submatrix 220 includes N_ldpc−K_ldpc number of columns (that is, K_ldpc^th column to (N_ldpc−1)^th column), and has a dual diagonal configuration. Accordingly, the degree of columns except the last column (that is, (N_ldpc−1)^th column) from among the columns included in the parity submatrix 220 is 2, and the degree of the last column is 1.

As a result, the information word submatrix 210 of the parity check matrix 200 may be defined by Tables 4 to 26, and the parity submatrix 220 may have a dual diagonal configuration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2 are permutated based on Equation 4 and Equation 5, the parity check matrix shown in FIG. 2 may be changed to a parity check matrix 300 shown in FIG. 3.

Q _ldpc ·i+j M·j+i(0≦i<M,0≦j<Q_ldpc)  (4)

K _ldpc +Q _ldpc ·k+l K _ldpc +M·l+k(0≦k<M,0≦l<Q_ldpc)  (5)

The method for permutating based on Equation 4 and Equation 5 will be explained below. Since row permutation and column permutation apply the same principle, the row permutation will be explained by the way of an example.

In the case of the row permutation, regarding the X^th row, i and j satisfying X=Q_ldpc×i+j are calculated and the X^th row is permutated by assigning the calculated i and j to M×j+i. For example, regarding the 7^th row, i and j satisfying 7=2×i+j are 3 and 1, respectively. Therefore, the 7^th row is permutated to the 13^th row (10×1+3=13).

When the row permutation and the column permutation are performed in the above-described method, the parity check matrix of FIG. 2 may be converted into the parity check matrix of FIG. 3.

Referring to FIG. 3, the parity check matrix 300 is divided into a plurality of partial blocks, and a quasi-cyclic matrix of M×M corresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×M are arranged in the plurality of partial blocks, constituting the parity check matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matrices of M×M, M number of columns may be referred to as a column block and M number of rows may be referred to as a row block. Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of N_{qc_column}=N_ldpc/M number of column blocks and N_{qc_row}=N_parity/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_{qc_column}−1)^th column block of the 0^th row block has a form shown in Equation 6 presented below:

$\begin{array}{cc}A=\left[\begin{array}{ccccc}0& 0& \dots & 0& 0\\ 1& 0& \dots & 0& 0\\ 0& 1& \dots & 0& 0\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ 0& 0& \dots & 1& 0\end{array}\right]& \left(6\right)\end{array}$

As described above, A 330 is an M×M matrix, values of the 0^th row and the (M−1)^th column are all “0”, and, regarding 0≦i≦(M−2), the (i+1)^th row of the i^th column is “1” and the other values are “0”.

Second, regarding 0≦i≦(N_ldpc−K_ldpc)/M−1 in the parity submatrix 320, the i^th row block of the (K_ldpc/M+i)^th column block is configured by a unit matrix I_M×M 340. In addition, regarding 0≦i≦(N_ldpc−K_ldpc)/M−2, the (i+1)^th row block of the (K_ldpc/M+i)^th column block is configured by a unit matrix I_M×M 340.

Third, a block 350 constituting the information word submatrix 310 may have a cyclic-shifted format of a cyclic matrix P, P^aij, or an added format of the cyclic-shifted matrix P^aij of the cyclic matrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted to the right by 1 may be expressed by Equation 7 presented below:

$\begin{array}{cc}P=\left[\begin{array}{ccccc}0& 1& 0& & 0\\ 0& 0& 1& \dots & 0\\ ⋮& ⋮& ⋮& & ⋮\\ 0& 0& 0& \dots & 1\\ 1& 0& 0& & 0\end{array}\right]& \left(7\right)\end{array}$

The cyclic matrix P is a square matrix having an M×M size and is a matrix in which a weight of each of M number of rows is 1 and a weight of each of M number of columns is 1. When a_ij is 0, the cyclic matrix P, that is, P⁰ indicates a unit matrix I_M×M, and when a_ij is ∞, P^∞ is a zero matrix.

A submatrix existing where the i^th row block and the j^th column block intersect in the parity check matrix 300 of FIG. 3 may be P^aij. Accordingly, i and j indicate the number of row blocks and the number of column blocks in the partial blocks corresponding to the information word. Accordingly, in the parity check matrix 300, the total number of columns is N_ldpc=M×N_{qc_column}, and the total number of rows is N_parity=M×N_{qc_row}. That is, the parity check matrix 300 is formed of N_{qc_column} number of column blocks and N_{qc_row} number of row blocks.

Referring back to FIG. 1, the encoder 110 may perform the LDPC encoding by using various code rates such as 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 may generate an LDPC codeword having various lengths such as 16200, 64800, etc., based on the length of the information word bits and the code rate.

In this case, the encoder 110 may perform the LDPC encoding by using the parity check matrix in which the information word submatrix is defined by Tables 4 to 26, and the parity submatrix has the dual diagonal configuration (that is, the parity check matrix shown in FIG. 2), or may perform the LDPC encoding by using the parity check matrix in which rows and columns are permutated from the parity check matrix of FIG. 2 based on Equations 4 and 5 (that is, the configuration of FIG. 3).

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem (BCH) encoding as well as LDPC encoding. To achieve this, the encoder 110 may further include a BCH encoder (not shown) to perform BCH encoding.

In this case, the encoder 110 may perform encoding in an order of BCH encoding and LDPC encoding. Specifically, the encoder 110 may add BCH parity bits to input bits by performing BCH encoding and LDPC-encodes the bits to which the BCH parity bits are added into information word bits, thereby generating the LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, the interleaver 120 receives the LDPC codeword from the encoder 110, and interleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword such that a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword (that is, a plurality of bit groups or a plurality of blocks) is mapped onto a predetermined bit of a modulation symbol.

Hereinafter, an interleaving rules used in the interleaver 120 will be explained in detail according to exemplary embodiments.

Exemplary Embodiment 1

Use of Block Interleaver

According to a first exemplary embodiment, the interleaver 120 may interleave the LDPC codeword in a method described below such that a bit included in a predetermined group from among a plurality of groups constituting the interleaved LDPC codeword is mapped onto a predetermined bit in a modulation symbol. A detailed description thereof is provided with reference to FIG. 4.

FIG. 4 is a block diagram to illustrate a configuration of an interleaver according to exemplary embodiment. Referring to FIG. 4, the interleaver 120 includes a parity interleaver 121, a group interleaver (or a group-wise interleaver 122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves parity bits constituting the LDPC codeword.

Specifically, when the LDPC codeword is generated based on the parity check matrix 200 having the configuration of FIG. 2, the parity interleaver 121 may interleave only the parity bits of the LDPC codeword by using Equations 8 presented below:

$\begin{array}{cc}{u}_i=c_i\mathrm{for}0\le i<K_{\mathrm{ldpc}},\mathrm{and}u_{K_{\mathrm{ldpc}}+M·t+s}=c_{K_{\mathrm{ldpc}}+Q_{\mathrm{ldpc}}·s+t}\mathrm{for}0\le s<M,0\le t<Q_{\mathrm{ldpc}},& \left(8\right)\end{array}$

where M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix 210, that is, the number of columns included in a column group (for example, M=360), and Q_ldpc is a size by which each column is cyclic-shifted in the information word submatrix 210. That is, the parity interleaver 121 performs parity interleaving with respect to the LDPC codeword c=(c₀, c₁, . . . , c_Nldpc−1), and outputs U=(u₀, u₁, . . . , u_Nldpc−1).

When the LDPC codeword encoded based on the parity check matrix 200 of FIG. 2 is parity-interleaved based on Equations 8, the parity-interleaved LDPC codeword is the same as the LDPC codeword encoded by the parity check matrix 300 of FIG. 3. Accordingly, when the LDPC codeword is generated based on the parity check matrix 300 of FIG. 3, the parity interleaver 121 may be omitted.

The LDPC codeword parity-interleaved after having been encoded based on the parity check matrix 200 of FIG. 2, or the LDPC codeword encoded based on the parity check matrix having the format of FIG. 3 may be characterized in that a predetermined number of continuous bits of the LDPC codeword have similar decoding characteristics (cycle distribution, a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on the basis of M number of continuous bits. Herein, M is an interval at which a pattern of a column group is repeated in the information word submatrix and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity check matrix should be “0”. This means that a sum of products of the i^th LDPC codeword bit, c_i(i=0, 1, . . . , N_ldpc−1) and the i^th column of the parity check matrix should be a “0” vector. Accordingly, the i^th LDPC codeword bit may be regarded as corresponding to the i^th column of the parity check matrix.

In a parity check matrix according to an exemplary embodiment, M number of columns belonging to the same group have the same degree, and have a substantially great cycle characteristic. Accordingly, since M number of continuous bits in an LDPC codeword correspond to the same column group of the parity check matrix and the cycle between M number of continuous bits is substantially great, these bits have a low decoding correlation.

Specifically, in the case of the parity check matrix of FIG. 2, since the information word submatrix 210 has the same characteristics on the basis of a column group of M number of columns (e.g., the columns of the same column group have the same degree distribution), the information word bits of the LDPC codeword encoded based on the parity check matrix 200 are formed of a plurality of bit groups each of which has M number of continuous bits of the same codeword characteristics. When the parity bits of the LDPC codeword are interleaved by the parity interleaver 121, the parity bits of the LDPC codeword may be formed of a plurality of bit groups each of which has M number of continuous bits having the same codeword characteristics.

In addition, in the case of the parity check matrix of FIG. 3, since the information word submatrix 310 and the parity submatrix 320 of the parity check matrix 300 have the same characteristics on the basis of a column group including M number of columns due to the row and column permutation, the information word bits and the parity bits of the LDPC codeword encoded based on the parity check matrix 300 are formed of a plurality of bit groups each of which has M number of continuous bits of the same codeword characteristics.

Herein, the row permutation does not influence the cycle characteristic or algebraic characteristic of the LDPC codeword such as a degree distribution, a minimum distance, etc. since the row permutation is just to rearrange the order of rows in the parity check matrix. In addition, since the column permutation is performed for the parity submatrix 320 to correspond to parity interleaving performed in the parity interleaver 121, the parity bits of the LDPC codeword encoded by the parity check matrix 300 of FIG. 3 are formed of a plurality of bit groups each of which has M number of continuous bits like the parity bits of the LDPC codeword encoded by the parity check matrix 200 of FIG. 2.

Accordingly, the bits constituting an LDPC codeword may have the same characteristics on the basis of M number of continuous bits, according to the present exemplary embodiment.

The group interleaver 122 may divide the parity-interleaved LDPC codeword into a plurality of groups and rearrange the order of the plurality of groups. That is, the group interleaver 122 interleaves the plurality of groups in group units.

To achieve this, the group interleaver 122 divides the parity-interleaved LDPC codeword into a plurality of groups by using Equation 9 or Equation 10 presented below.

$\begin{array}{cc}X_j=\left\{u_kj=\lfloor \frac{k}{360}\rfloor ,0\le k<N_{\mathrm{ldpc}}\right\}\mathrm{for}0\le j<N_{\mathrm{group}}& \left(9\right)\\ X_j=\left\{u_k360j\le k<360\left(j+1\right),0\le k<N_{\mathrm{ldpc}}\right\}\mathrm{for}0\le j<N_{\mathrm{group}}& \left(10\right)\end{array}$

where N_group is the total number of groups, X_j is the j^th group, and u_k is the k^th LDPC codeword bit input to the group interleaver 122. In addition,

$\lfloor \frac{k}{360}\rfloor$

is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M at which the pattern of a column group is repeated in the information word submatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of groups may be as shown in FIG. 5.

Referring to FIG. 5, the LDPC codeword is divided into the plurality of groups and each group is formed of M number of continuous bits.

Specifically, since the LDPC codeword is divided by M number of continuous bits, K_ldpc number of information word bits are divided into (K_ldpc/M) number of groups and N_ldpc−K_ldpc number of parity bits are divided into (N_ldpc−K_ldpc)/M number of groups. Accordingly, the LDPC codeword may be divided into (N_ldpc/M) number of groups in total.

For example, when M=360 and the length N_ldpc of the LDPC codeword is 64800, the number of groups N_groups is 180, and, when the length N_ldpc of the LDPC codeword is 16200, the number of groups N_group is 45.

As described above, the group interleaver 122 divides the LDPC codeword such that M number of continuous bits are included in a same group since the LDPC codeword has the same codeword characteristics on the basis of M number of continuous bits. Accordingly, when the LDPC codeword is grouped by M number of continuous bits, the bits having the same codeword characteristics belong to the same group.

Meanwhile, in the above exemplary embodiment, M number of bits forms each group, but this is only an example. The number of bits forming each group may vary.

For example, the number of bits forming each group may be a divisor of M. In other words, the number of bits forming each group may be a divisor of the number of columns constituting a column group of an information word submatrix of a parity check matrix. In this case, each group may consist of the number of bits which is a divisor of M. For example, if the number of columns forming a column group of an information word submatrix is 360, that is, M=360, the group interleaver 122 may divide a LDPC codeword into a plurality of groups so that the number of bits constituting each group becomes one of divisors of 360.

However, in this specification, only a case where the number of bits forming a group is M will be described for convenience of explanation,

Thereafter, the group interleaver 122 interleaves the LDPC codeword in group units. That is, the group interleaver 122 changes positions of the plurality of groups constituting the LDPC codeword and rearranges the order of the plurality of groups constituting the LDPC codeword.

In this case, the group interleaver 122 may rearrange the order of the plurality of groups by using Equation 11 presented below:

Y _j =X _π(j)(0≦j<N_group)  (11),

where X_j is the j^th group before group interleaving, and Y_j is the j^th group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 27 to 41 presented below.

For example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 27 or 28 presented below:

TABLE 27
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	7	17	33	31	26	30	32	41	28	8	24	42	20	9	35	43	22	12	38	3	5	14	37
12/15, 13/15	40	19	16	27	39	25	4	21	1	23	18	36	0	6	11	34	2	29	15	30	13	4

TABLE 28
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	6	34	11	21	12	8	9	21	22	2	10	15	7	14	20	13	32	17	18	3	19	16	25
12/15, 13/15	24	43	40	33	36	37	39	44	41	42	4	0	20	31	5	33	35	12	28	26	27	29

In the case of Table 27, Equation 11 may be expressed as Y₀=X_π(0)=X₇, Y₁=X_π(1)=X₁₇, Y₂=X_π(2)=X₃₃, . . . , Y₄₃=X_π(43)=X₁₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 7^th group to the 0^th group, the 17^th group to the 1^st group, the 33^rd group to the 2^nd group, . . . , the 13^th group to the 43-^rd group, and the 44^th group to the 44^th group.

In the case of Table 28, Equation 11 may be expressed as Y₀=X_π(0)=X₆, Y₁=X_π(1)=X₃₄, Y₂=X_π(2)=X₁₁, . . . , Y₄₃=X_π(43)=X₂₇, and Y₄₄=X_π(44)=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 6^th group to the 0^th group, the 34^th group to the 1^st group, the 11^th group to the 2^nd group, . . . , the 27^th group to the 43^rd group, and the 29^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 29 or 30 presented below:

TABLE 29
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	32	4	23	27	35	24	16	39	5	22	33	40	18	13	8	6	37	34	0	15	21	38	30
8/15, 9/15	26	14	17	10	31	25	28	12	1	29	9	41	3	20	19	36	11	7	2	42	43	44

TABLE 30
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	32	16	18	0	14	12	20	4	39	13	15	17	1	19	23	5	8	21	10	29	36	27	22
8/15, 9/15	6	38	31	9	11	35	33	37	30	25	41	7	24	40	34	26	28	3	2	42	43	44

In the case of Table 29, Equation 11 may be expressed as Y₀=X_π(0)=X₃₂, Y₁=X_π(1)=X₄, Y₂=X_π(2)=X₂₃, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 32^nd group to the 0^th group, the 4^th group to the 1^st group, the 23^rd group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 30, Equation 11 may be expressed as Y₀=X_π(0)=X₃₂, Y₁=X_π(1)=X₁₆, Y₂=X_π(2)=X₁₈, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 32^nd group to the 0^th group, the 16^th group to the 1^st group, the 18^th group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 31 or 32 presented below:

TABLE 31
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	28	6	15	8	0	22	37	35	21	26	7	12	27	1	32	33	13	11	10	18	34	9	39
12/15, 13/15	38	24	17	29	25	5	16	30	2	4	19	23	14	20	3	31	36	40	41	42	43	44

TABLE 32
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	21	8	30	0	20	9	1	22	23	24	13	11	12	14	10	17	16	6	15	2	33	18	31
12/15, 13/15	7	34	38	37	5	19	36	44	39	41	43	40	42	3	35	32	4	25	26	27	28	29

In the case of Table 31, Equation 11 may be expressed as Y₀=X_π(0)=X₂₈, Y₁=X_π(1)=X₆, Y₂=X_π(2)=X₁₅, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 28^th group to the 0^th group, the 6^th group to the 1^st group, the 15^th group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 32, Equation 11 may be expressed as Y₀=X_π(0)=X₂₁, Y₁=X_π(1)=X₈, Y₂=X_π(2)=X₃₀, β, Y₄₃=X_π(43)=X₂₈, and Y₄₄=X_π(44)=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 21^st group to the 0^th group, the 8^th group to the 1^st group, the 30^th group to the 2^nd group, . . . , the 28^th group to the 43^rd group, and the 29^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 33 or 34 presented below:

TABLE 33
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	16	13	1	25	24	33	4	29	32	30	0	17	22	18	8	9	27	11	37	35	12	15	10
8/15, 9/15	20	5	6	36	38	2	26	14	7	19	3	21	23	31	34	28	39	40	41	42	43	44

TABLE 34
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	16	12	14	19	34	13	15	17	8	11	4	6	7	44	9	5	1	21	18	31	40	10	28
8/15, 9/15	20	24	27	41	32	30	42	26	36	0	23	35	29	33	25	22	42	2	3	37	38	39

In the case of Table 33, Equation 11 may be expressed as Y₀=X_π(0)=X₁₆, Y₁=X_π(1)=X₁₃, Y₂=X_π(2)=X₁, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 16^th group to the 0^th group, the 13^th group to the 1^st group, the 1^st group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 34, Equation 11 may be expressed as Y₀=X_π(0)=X₁₆, Y₁=X_π(1)=X₁₂, Y₂=X_π(2)=X₁₄, β, Y₄₃=X_π(43)=X₃₈, and Y₄₄=X_π(44)=X₃₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 16^th group to the 0^th group, the 12^th group to the 1^st group, the 14^th group to the 2^nd group, . . . , the 38^th group to the 43^rd group, and the 39^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 35 or 36 presented below:

TABLE 35
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	48	4	15	97	108	76	1	174	81	0	58	71
7/15,	138	35	62	43	16	153	73	178	165	21	49	91
8/15,	110	80	58	42	40	103	159	83	127	111	63	89
9/15	123	79	141	51	21	17	45	126	150	3	168	41
	14	131	82	134	55	33	50	84	28	105	6	145
	30	151	18	148	129	53	100	22	107	16	170	143
	37	24	130	136	161	75	29	9	47	60	162	148
	18	85	88	135	116	12	163	20	46	87	54	139
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	120	175	167	114	65	95	101	19	112	109	152
	7/15,	5	109	99	72	149	78	36	25	56	156	155
	8/15,	11	52	144	141	133	154	44	96	93	66	122
	9/15	106	124	54	147	78	8	118	113	39	69	140
		7	27	132	92	115	164	74	10	68	102	67
		121	38	57	95	90	172	81	158	171	32	119
		137	157	70	104	31	34	166	239	117	125	2
		54	72	100	176	177	178	179

TABLE 36
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	48	61	65	35	23	26	58	63	44	51	41	113
7/15,	0	98	62	49	36	42	89	96	21	106	39	33
8/15,	101	43	91	25	40	11	93	17	124	69	50	132
9/15	86	5	56	103	52	66	45	64	140	84	92	30
	169	156	159	144	122	126	147	14	28	115	151	16
	155	83	142	123	150	78	131	105	164	18	170	81
	127	135	79	3	8	82	6	74	140	143	158	161
	154	141	168	118	134	145	10	129	121	171	75	157
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	55	7	68	53	38	32	29	70	2	20	4
	7/15,	27	102	100	57	119	9	104	13	46	15	59
	8/15,	67	22	95	37	47	31	85	87	97	71	19
	9/15	107	90	24	60	34	88	94	108	120	112	153
		172	130	162	166	135	139	76	175	109	73	99
		136	146	128	116	54	1	167	152	173	77	110
		137	117	12	72	174	114	138	165	149	80	111
		125	163	160	176	177	178	179

In the case of Table 35, Equation 11 may be expressed as Y₀=X_π(0)=X₄₈, Y₁=X_π(1)=X₄, Y₂=X_π(2)=X₁₅, . . . , Y₁₇₈=X_π(178)=X₁₇₈, and Y₁₇₉=X_π(179)=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 48^th group to the 0^th group, the 4^th group to the 1^st group, the 15^th group to the 2^nd group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In the case of Table 36, Equation 11 may be expressed as Y₀=X_π(0)=X₄₈, Y₁=X_π(1)=X₆₁, Y₂=X_π(2)=X₆₅, . . . , Y₁₇₈=X_π(178)=X₁₇₈, and Y₁₇₉=X_π(179)=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 48^th group to the 0^th group, the 61^st group to the 1^st group, the 65^th group to the 2^nd group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 37 presented below:

TABLE 37
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15	53	3	28	46	68	15	43	29	49	0	58	42
	63	51	57	67	54	48	60	61	59	70	45	55
	151	178	119	50	105	84	27	10	25	165	174	44
	170	86	141	139	89	107	12	73	79	118	167	166
	157	163	117	74	90	158	153	81	6	104	88	123
	38	75	100	76	136	20	134	94	35	132	152	156
	85	155	131	176	150	130	124	113	173	91	95	11
	148	116	161	80	177	83	4	133	122	160	121	128
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15	23	1	47	32	7	36	34	14	37	18	71
		56	66	64	17	40	69	52	62	65	135	106
		21	19	145	112	30	140	16	13	172	154	115
		72	171	82	96	127	142	162	164	159	179	5
		99	101	144	97	168	137	8	98	11	39	87
		146	103	77	2	41	114	143	103	109	175	125
		93	92	149	138	126	120	147	129	102	33	9
		78	111	169	22	24	26	31

In the case of Table 37, Equation 11 may be expressed as Y₀=X_π(0)=X₅₃, Y₁=X_π(1)=X₃, Y₂=X_π(2)=X₂₈, . . . , Y₁₇₈=X_π(178)=X₂₆, and Y₁₇₉=X_π(179)=X₃₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 53^rd group to the 0^th group, the 3^rd group to the 1^st group, the 28^th group to the 2^nd group, . . . , the 26^th group to the 178^th group, and the 31st group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 37 presented below:

TABLE 38
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
8/15	71	104	84	69	94	93	74	89	57	58	56	59
	87	62	10	75	12	85	17	47	80	7	60	68
	76	67	66	98	52	79	164	46	90	120	51	82
	49	28	23	31	50	14	25	65	40	30	19	24
	138	108	166	149	144	123	169	148	112	156	167	100
	111	27	137	26	160	21	20	163	162	32	134	22
	159	109	101	135	153	116	106	124	102	146	168	130
	174	170	9	131	125	3	118	161	81	126	0	150
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	8/15	173	86	132	83	77	55	64	45	54	41	36
		6	92	43	13	70	91	48	61	1	38	110
		133	44	39	115	165	37	119	155	78	63	53
		88	29	95	73	2	8	72	140	176	142	158
		114	177	179	147	105	178	35	34	33	97	172
		151	136	15	42	121	175	145	127	96	143	141
		152	139	99	113	171	154	122	128	107	157	103
		129	117	21	4	5	16	18

In the case of Table 38, Equation 11 may be expressed as Y₀=X_π(0)=X₇₁, Y₁=X_π(1)=X_1o4, Y₂=X_π(2)=X₈₄, . . . , Y₁₇₈=X_π(178)=X₁₆, and Y₁₇₉=X_π(179)=X₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 71^st group to the 0^th group, the 104^th group to the 1^st group, the 84^th group to the 2^nd group, . . . , the 16^th group to the 178^th group, and the 18^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 39 presented below. In particular, when the encoder 110 performs the LDPC encoding based on the parity check matrix defined by Table 24, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 39:

TABLE 39
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	111	65	78	49	68	44	119	96	97	108	69	114
	101	105	45	55	98	93	41	109	42	110	87	36
	94	60	104	19	117	46	102	75	91	76	50	5
	81	84	0	2	21	80	26	33	70	74	57	88
	47	113	151	52	86	154	6	40	11	107	31	177
	161	162	22	133	174	82	124	160	18	158	176	168
	163	146	138	139	17	143	159	25	10	152	145	59
	126	121	147	135	140	137	144	175	157	127	9	171
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	51	66	29	62	73	106	54	103	43	89	39
		90	32	116	4	20	23	38	71	8	34	115
		79	92	35	95	99	53	37	72	100	58	56
		13	27	14	77	7	30	61	48	63	67	112
		132	64	136	131	150	16	155	148	1	125	24
		149	134	178	169	128	173	3	130	12	15	172
		153	179	166	129	120	142	141	165	167	170	164
		122	123	156	28	83	85	118

In the case of Table 39, Equation 11 may be expressed as Y₀=X_π(0)=X₁₁₁, Y₁=X_π(1)=X₆₅, Y₂=X_π(2)=X₇₈, . . . , Y₁₇₈=X_π(178)=X₈₅, and Y₁₇₉=X_π(179)=X₁₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 111^th group to the 0^th group, the 65^th group to the 1^st group, the 78^th group to the 2^nd group, . . . , the 85^th group to the 178^th group, and the 118^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 40 presented below. In particular, when the encoder 110 performs the LDPC encoding based on the parity check matrix defined by Table 25, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 40:

TABLE 40
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	89	64	50	28	32	26	52	98	66	31	90	59
	118	84	95	81	7	96	36	18	3	65	1	116
	35	82	67	33	44	48	91	112	49	78	55	106
	2	23	86	105	53	38	62	110	4	83	15	87
	103	158	93	58	101	34	77	61	164	173	132	39
	159	14	143	139	146	161	130	129	171	179	157	148
	168	136	160	170	5	150	124	144	156	167	123	149
	131	122	10	155	154	174	162	80	133	16	22	128
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	70	17	76	117	54	68	11	43	57	92	20
		97	119	94	100	107	75	69	63	30	72	109
		46	108	51	113	102	71	40	111	104	74	21
		73	79	115	6	56	42	47	85	99	145	114
		151	88	60	41	37	45	172	166	152	127	169
		9	138	147	0	135	13	177	178	19	137	12
		134	142	121	141	165	126	125	140	153	175	176
		163	120	8	24	25	27	29

In the case of Table 40, Equation 11 may be expressed as Y₀=X_π(0)=X₈₉, Y₁=X_π(1)=X₆₄, Y₂=X_π(2)=X₅₀, . . . , Y₁₇₈=X_π(178)=X₂₇, and Y₁₇₉=X_π(179)=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 89^th group to the 0^th group, the 64^th group to the 1^st group, the 50^th group to the 2^nd group, . . . , the 27^th group to the 178^th group, and the 29^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 41 presented below:

TABLE 41
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
12/15	51	122	91	111	95	100	119	130	78	57	65	26
	14	3	21	71	134	2	0	140	106	7	118	23
	129	107	30	45	137	114	37	87	53	85	101	141
	97	38	124	86	33	74	32	29	128	67	104	80
	54	40	81	103	121	76	44	84	96	123	154	98
	36	59	90	79	52	133	60	92	139	110	27	73
	164	158	157	160	150	171	167	145	151	153	9	155
	148	172	178	24	22	179	4	163	174	173	19	10
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	12/15	61	126	105	143	70	132	39	102	115	116	6
		35	20	17	50	48	112	13	66	5	75	42
		120	99	88	117	64	28	135	138	108	113	58
		127	56	34	89	94	49	55	93	136	68	62
		82	142	45	169	131	72	47	69	125	31	83
		43	77	109	63	41	168	147	161	165	175	162
		170	146	166	149	15	159	11	176	152	156	144
		177	12	16	1	8	18	25

In the case of Table 41, Equation 11 may be expressed as Y₀=X_π(0)=X₅₁, Y₁=X_π(1)=X₁₂₂, Y₂=X_π(2)=X₉₁, . . . , Y₁₇₈=X_π(178)=X₁₈, and Y₁₇₉=X_π(179)=X₂₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 51^st group to the 0^th group, the 122^nd group to the 1^st group, the 91^st group to the 2^nd group, . . . , the 18^th group to the 178^th group, and the 25^th group to the 179^th group.

As described above, it is possible to rearrange the order of column groups in the parity check matrix having the shape of FIGS. 2 and 3, and a column group corresponds to a bit group. Accordingly, if the order of column groups is changed in the parity check matrix, the order of bit groups may also be changed accordingly.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups by using Equation 11 and Tables 27 to 41.

On the other hand, since the order of the groups constituting the LDPC codeword is rearranged by the group interleaver 122, and then the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 27 to 41 in relation to π(j).

In addition, the group interleaver 122 may interleave the LDPC codeword in group units by using Equation 12 presented below:

Y _π(j))=X_j(0≦j<N_group)  (12),

where X_j is the j^th group before group interleaving, and Y_j is the j^th group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 42 to 51 presented below.

For example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 42 or 43 presented below:

TABLE 42
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	35	31	39	19	29	20	36	0	9	13	5	37	17	43	21	41	25	1	33	24	12	30	16
12/15, 13/15	32	10	28	4	26	8	40	42	3	6	2	38	14	34	22	18	27	23	7	11	15	44

TABLE 43
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	34	49	9	19	13	37	0	12	5	6	10	2	4	15	13	12	21	17	18	20	35	3	8
12/15, 13/15	7	23	22	42	41	41	44	14	38	16	18	1	17	27	28	23	29	25	31	32	21	50

In the case of Table 42, Equation 12 may be expressed as X₀=Y_π(0)=Y₃₅, X₁=Y_π(1)=Y₃₁, X₂=Y_π(2)=Y₃₉, . . . , X₄₃=Y_π(43)=Y₁₅, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 35^th group, the 1^st group to the 31^st group, the 2^nd group to the 39^th group, . . . , the 43^rd group to the 15^th group, and the 44^th group to the 44^th group.

In the case of Table 43, Equation 12 may be expressed as X₀=Y_π(0)=Y₃₄, X₁=Y_π(1)=Y₄₀, X₂=Y_π(2)=Y₉, . . . , X₄₃=Y_π(43)=Y₂₄, and X₄₄=Y_π(44)=Y₃₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 34^th group, the 1^st group to the 40^th group, the 2^nd group to the 9^th group, . . . , the 43^rd group to the 24^th group, and the 44^th group to the 30^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 44 or 45 presented below:

TABLE 44
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	18	31	41	35	1	8	15	40	14	33	26	39	30	13	24	19	6	25	12	37	36	20	9
8/15, 9/15	2	5	28	23	3	29	32	22	27	0	10	17	4	38	16	21	7	11	34	42	43	44

TABLE 45
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	3	12	41	40	7	15	23	34	16	26	18	27	5	9	4	10	1	31	2	13	6	17	22
8/15, 9/15	14	35	32	38	21	39	19	31	25	0	29	37	28	20	30	24	8	36	33	42	43	44

In the case of Table 44, Equation 12 may be expressed as X₀=Y_π(0)=Y₁₈, X₁=Y_π(1)=Y₃₁, X₂=Y_π(2)=Y₄₁, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 18^th group, the 1^st group to the 31^st group, the 2nd group to the 41^th group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 45, Equation 12 may be expressed as X₀=Y_π(0)=Y₃, X₁=Y_π(1)=Y₁₂, X₂=Y_π(2)=Y₄₁, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 3^rd group, the 1^st group to the 12^th group, the 2^nd group to the 41^st group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 46 or 47 presented below:

TABLE 46
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	4	13	31	37	32	28	1	10	3	21	18	17	11	16	35	2	29	25	19	33	36	8	5
12/15, 13/15	34	24	27	9	12	0	26	20	38	14	15	20	7	39	6	23	22	40	41	42	43	44

TABLE 47
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	3	6	19	36	39	27	17	23	1	5	14	11	12	10	13	18	16	15	21	28	4	0	7
12/15, 13/15	8	9	40	41	42	43	44	2	22	38	20	24	37	29	26	25	31	34	32	35	33	30

In the case of Table 46, Equation 12 may be expressed as X₀=Y_π(0)=Y₄, X₁=Y_π(1)=Y₁₃, X₂=Y_π(2)=Y₃₁, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 4^th group, the 1^st group to the 13^th group, the 2^nd group to the 31^st group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 47, Equation 12 may be expressed as X₀=Y_π(0)=Y₃, X₁=Y_π(1)=Y₆, X₂=Y_π(2)=Y₁₉, . . . , X₄₃=Y_π(43)=Y₃₃, and X₄₄=Y_π(44)=Y₃₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 3^rd group, the 1^st group to the 6^th group, the 2^nd group to the 19^th group, . . . , the 43^rd group to the 33^rd group, and the 44^th group to the 30^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 48 or 49 presented below:

TABLE 48
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	10	2	28	33	6	24	25	31	14	15	22	17	20	1	30	21	0	11	13	32	23	34	12
8/15, 9/15	35	4	3	29	16	38	7	9	36	8	5	37	19	26	18	27	39	40	41	42	43	44

TABLE 49
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	32	16	40	41	10	15	11	12	8	14	21	9	1	5	2	6	0	7	18	3	23	17	38
8/15, 9/15	33	24	37	30	25	22	35	28	19	27	36	4	34	31	42	43	44	20	26	29	39	23

In the case of Table 48, Equation 12 may be expressed as X₀=Y_π(0)=Y₁₀, X₁=Y_π(1)=Y₂, X₂=Y_π(2)=Y₂₈, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 10^th group, the 1^st group to the 2^nd group, the 2^nd group to the 28^th group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 49, Equation 12 may be expressed as X₀=Y_π(0)=Y₃₂, X₁=Y_π(1)=Y₁₆, X₂=Y_π(2)=Y₄₀, . . . , X₄₃=Y_π(43)=Y₃₉, and X₄₄=Y_π(44)=Y₁₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 32^nd group, the 1^st group to the 16^th group, the 2^nd group to the 40^th group, . . . , the 43^rd group to the 39^th group, and the 44^th group to the 13^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 50 or 51 presented below:

TABLE 50
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	9	6	160	78	1	35	102	104	86	145	111	58
7/15,	32	139	42	40	105	100	144	115	154	136	97	155
8/15,	169	146	0	33	98	72	59	120	173	96	43	129
9/15	90	152	11	174	29	110	143	5	38	85	70	47
	107	66	171	130	65	3	17	37	121	18	113	51
	108	165	158	87	137	12	127	68	69	82	159	76
	23	172	91	71	61	126	60	103	149	84	118	39
	142	148	167	109	31	156	14	79	36	125	135	132
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	166	161	92	2	124	74	117	19	168	73	122
	7/15,	24	41	138	128	89	50	80	49	26	64	75
	8/15,	48	10	147	8	25	56	83	16	67	114	112
	9/15	133	94	53	99	162	27	170	163	57	131	34
		153	101	81	123	4	21	46	55	20	88	15
		54	157	119	140	93	106	62	95	164	141	150
		77	116	22	28	63	45	44	151	134	52	175
		30	7	13	179	178	177	176

TABLE 51
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	23	132	20	141	22	70	144	13	142	46	167	51
7/15,	4	83	9	3	35	100	18	80	63	17	34	83
8/15	43	62	0	26	56	9	73	15	171	12	31	38
9/15	55	19	57	152	113	145	171	110	236	120	140	158
	79	52	87	60	30	6	24	114	37	48	36	71
	101	110	151	162	39	89	169	56	118	54	173	97
	156	109	77	162	117	147	95	156	128	55	145	155
	149	106	174	123	157	107	122	163	92	125	170	104
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	152	42	99	44	103	51	124	68	21	31	39
	7/15,	3	27	61	16	23	30	10	28	47	8	75
	8/15	6	45	84	1	25	7	76	2	74	58	14
	9/15	126	143	216	78	64	69	65	85	29	82	48
		41	122	12	81	88	312	137	110	90	11	113
		138	123	168	103	121	57	139	163	104	127	150
		119	102	134	91	165	115	51	172	143	54	175
		135	154	111	276	177	378	179

In the case of Table 50, Equation 12 may be expressed as X₀=Y_π(0)=Y₉, X₁=Y_π(1)=Y₆, X₂=Y_π(2)=Y₁₆₀, . . . , X₁₇₈=Y_π(178)=Y₁₇₇, and X₁₇₉=Y_π(179)=Y₁₇₆ Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 9^th group, the 1^st group to the 6^th group, the 2^nd group to the 160^th group, . . . , the 178^th group to the 177^th group, and the 179^th group to the 176^th group.

In the case of Table 51, Equation 12 may be expressed as X₀=Y_π(0)=Y₂₃, X₁=Y_π(1)=Y₁₃₂, X₂=Y_π(2)=Y₂₀, . . . , X₁₇₈=Y_π(178)=Y₁₇₈, and X₁₇₉=Y_π(179)=Y₁₇₉ Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 23^rd group, the 1^st group to the 132^nd group, the 2^nd group to the 20^th group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 52 presented below:

TABLE 52
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15	9	13	130	1	167	91	100	16	110	160	53	112
	12	177	54	178	52	2	7	62	179	15	159	18
	3	14	28	8	49	24	41	0	27	34	35	25
	40	32	22	81	76	95	116	118	129	173	77	164
	151	150	122	148	84	107	111	104	117	105	158	128
	68	162	94	78	48	155	171	169	103	144	137	154
	153	72	63	71	86	133	106	60	127	156	161	152
	163	87	93	88	55	80	79	108	175	69	82	66
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15	75	65	19	5	64	38	21	59	120	58	176
		123	17	20	115	113	39	131	11	6	57	33
		10	31	29	30	42	23	37	43	36	26	4
		99	83	155	51	138	70	114	102	73	96	147
		101	50	45	74	134	135	149	174	61	145	132
		85	172	157	143	140	124	168	121	44	119	109
		142	46	125	98	67	139	126	92	97	89	170
		146	56	136	141	165	47	90

In the case of Table 52, Equation 12 may be expressed as X₀=Y_π(0)=Y₉, X₁=Y_π(1)=Y₁₃, X₂=Y_π(2)=Y₁₃₀, . . . , X₁₇₈=Y_π(178)=Y₄₇, and X₁₇₉=Y_π(179)=Y₉₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 9^th group, the 1^st group to the 13^th group, the 2^nd group to the 130^th group, . . . , the 178^th group to the 47^th group, and the 179^th group to the 90^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 53 presented below:

TABLE 53
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
8/15	171	43	85	166	176	177	35	32	86	163	25	175
	71	80	75	118	116	70	82	78	72	124	112	111
	53	30	41	69	73	56	50	68	20	17	10	8
	3	39	0	87	84	6	26	46	16	66	51	31
	36	5	4	83	135	113	49	152	101	140	146	160
	61	143	174	167	64	55	131	156	97	145	165	170
	92	151	88	137	90	136	96	133	147	107	99	95
	168	123	122	52	62	94	102	148	98	162	154	114
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	8/15	27	38	74	129	178	29	179	79	121	120	126
		110	22	63	44	60	77	21	130	37	59	19
		9	11	33	42	24	67	18	76	48	47	34
		169	57	15	2	28	13	23	81	7	54	40
		1	108	144	158	93	139	45	115	100	153	104
		134	157	173	149	164	14	58	175	141	128	117
		172	127	150	142	155	65	101	159	91	138	119
		12	161	132	89	105	109	106

In the case of Table 53, Equation 12 may be expressed as X₀=Y_π(0)=Y₁₇₁, X₁=Y_π(1)=Y₄₃, X₂=Y_π(2)=Y₈₅, . . . , X₁₇₈=Y_π(178)=Y₁₀₉, and X₁₇₉=Y_π(179)=Y₁₀₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 171^st group, the 1^st group to the 43^rd group, the 2^nd group to the 85^th group, . . . , the 178^th group to the 109^th group, and the 179^th group to the 106^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 54 presented below:

TABLE 54
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	71	112	72	133	38	57	98	85	43	171	146	100
	40	114	145	75	82	176	14	86	102	36	76	44
	51	92	88	3	56	12	95	63	18	26	68	79
	10	77	42	65	16	78	53	55	84	2	58	74
	59	28	46	61	7	8	27	62	66	23	52	19
	45	37	50	179	6	154	162	173	174	121	113	161
	140	141	165	156	155	143	167	148	139	163	111	127
	115	116	138	160	157	152	158	126	130	159	172	137
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	135	81	83	136	109	142	123	49	39	73	117
		60	34	64	41	22	99	29	31	20	5	25
		67	149	47	87	15	89	105	1	13	90	4
		69	120	177	70	178	96	33	80	21	35	54
		48	24	17	101	9	30	32	0	91	93	11
		170	131	153	134	107	104	118	128	164	106	166
		108	94	147	150	97	110	175	169	124	144	122
		132	119	168	125	103	129	151

In the case of Table 54, Equation 12 may be expressed as X₀=Y_π(0)=Y₇₁, X₁=Y_π(1)=Y₁₁₂, X₂=Y_π(2)=Y₇₂, . . . , X₁₇₈=Y_π(178)=Y₁₂₉, and X₁₇₉=Y_π(179)=Y₁₅₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 71^st group, the 1^st group to the 112^th group, the 2^nd group to the 72^nd group, . . . , the 178^th group to the 129^th group, and the 179^th group to the 151^st group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 55 presented below:

TABLE 55
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	130	33	69	31	77	142	84	27	175	127	163	18
	70	176	177	5	178	3	179	43	9	4	49	97
	58	87	51	54	2	60	6	73	16	56	85	20
	41	12	63	44	81	57	40	14	98	55	82	168
	21	94	37	25	28	35	7	89	38	96	82	92
	83	34	15	23	36	174	152	162	148	144	156	155
	128	118	157	153	151	117	145	90	119	129	126	149
	120	167	173	100	154	111	147	138	114	141	123	110
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	137	132	116	79	170	13	30	135	22	68	171
		46	29	108	74	103	64	107	86	19	50	109
		95	11	106	99	75	42	1	32	8	48	17
		26	47	78	24	88	71	80	105	0	10	52
		56	72	57	39	59	45	76	65	53	61	91
		113	172	122	121	161	102	169	150	131	139	136
		143	104	112	158	165	164	146	125	93	115	140
		101	166	159	160	133	134	124

In the case of Table 55, Equation 12 may be expressed as X₀=Y_π(0)=Y₁₃₀, X₁=Y_π(1)=Y₃₃, X₂=Y_π(2)=Y₆₉, . . . , X₁₇₈=Y_π(178)=Y₁₃₄, and X₁₇₉=Y_π(179)=Y₁₂₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 130^th group, the 1^st group to the 33^rd group, the 2^nd group to the 69^th group, . . . , the 178^th group to the 134^th group, and the 179^th group to the 124^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 56 presented below:

TABLE 56
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
12/15	29	176	28	24	167	43	22	32	177	148	172	156
	34	164	179	11	125	63	76	48	113	75	73	83
	105	110	39	85	38	0	119	54	92	87	82	9
	111	16	26	109	126	74	44	97	128	8	118	80
	122	88	85	4	100	69	103	59	5	56	19	95
	20	21	61	33	6	58	96	1	101	72	112	13
	65	123	30	57	105	15	160	145	151	133	161	153
	134	137	168	138	135	152	144	132	107	150	143	162
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	12/15	174	41	23	154	175	37	178	171	36	25	165
		35	115	52	70	18	93	131	45	127	98	49
		68	116	121	12	91	130	62	10	42	78	90
		94	104	114	99	55	72	53	60	84	117	2
		79	14	31	47	66	129	124	3	40	67	51
		81	77	46	7	108	17	120	27	64	89	50
		142	146	158	147	102	149	159	140	139	155	141
		170	169	136	157	173	163	166

In the case of Table 56, Equation 12 may be expressed as X₀=Y_π(0)=Y₂₉, X₁=Y_π(1)=Y₁₇₆, X₂=Y_π(2)=Y₂₈, . . . , X₁₇₈=Y_π(178)=Y₁₆₃, and X₁₇₉=Y_π(179)=Y₁₆₆ Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^th group to the 29^th group, the 1^st group to the 176^th group, the 2^nd group to the 28^th group, . . . , the 178^th group to the 163^rd group, and the 179^th group to the 166^th group.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups by using Equation 12 and Tables 42 to 56.

Since the order of the groups constituting the LDPC codeword is rearranged by the group interleaver 122, and then the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 42 to 56 in relation to π(j).

The LDPC codeword which is group-interleaved in the above-described method is illustrated in FIG. 6. Comparing the LDPC codeword of FIG. 6 and the LDPC codeword of FIG. 5 before group interleaving, it can be seen that the order of the plurality of groups constituting the LDPC codeword is rearranged.

That is, as shown in FIGS. 5 and 6, the groups of the LDPC codeword are arranged in order of group X₀, group X₁, . . . , group X_Ngroup-1 before being group-interleaved, and are arranged in an order of group Y₀, group Y₁, . . . , group Y_Ngroup-1 after being group-interleaved. In this case, the order of arranging the groups by the group interleaving may be determined based on Tables 27 to 56.

The group twist interleaver 123 interleaves bits in a same group. That is, the group twist interleaver 123 may rearrange the order of the bits in the same group by changing the order of the bits in the same group.

In this case, the group twist interleaver 123 may rearrange the order of the bits in the same group by cyclic-shifting a predetermined number of bits from among the bits in the same group.

For example, as shown in FIG. 7, the group twist interleaver 123 may cyclic-shift bits included in the group Y₁ to the right by 1 bit. In this case, the bits located in the 0^th position, the 1^st position, the 2^nd position, . . . , the 358^th position, and the 359^th position in the group Y₁ as shown in FIG. 7 are cyclic-shifted to the right by 1 bit. As a result, the bit located in the 359^th position before being cyclic-shifted is located in the front of the group Y₁ and the bits located in the 0^th position, the 1^st position, the 2^nd position, . . . , the 358^th position before being cyclic-shifted are shifted to the right serially by 1 bit and located.

In addition, the group twist interleaver 123 may rearrange the order of bits in each group by cyclic-shifting a different number of bits in each group.

For example, the group twist interleaver 123 may cyclic-shift the bits included in the group Y₁ to the right by 1 bit, and may cyclic-shift the bits included in the group Y₂ to the right by 3 bits.

Changing the order of the bits in the same group as described above is referred to as a group twist. The group twist may be performed to prevent bits mapped onto a single modulation symbol from being connected to a single check node. Accordingly, the group twist interleaver 123 may be omitted according to circumstances.

In addition, the group twist interleaver 123 is placed after the group interleaver 122 in the above-described example. However, this is merely an example. That is, the group twist interleaver 123 changes only the order of bits in a certain group and does not change the order of the groups. Therefore, the group twist interleaver 123 may be placed before the group interleaver 122.

The block interleaver 124 interleaves the plurality of groups the order of which has been rearranged. Specifically, the block interleaver 124 may interleave the plurality of groups the order of which has been rearranged by the group interleaver 122.

That is, the group twist interleaver 123 changes only the order of bits in the same group and does not change the order of groups by interleaving. Accordingly, the order of the groups to be block-interleaved by the block interleaver 124 may be determined by the group interleaver 122. Specifically, the order of the groups to be block-interleaved by the block interleaver 124 may be determined by π(j) defined in Tables 27 to 56.

The block interleaver 124 may interleave the plurality of groups the order of which has been rearranged by using at least one column and a plurality of rows.

Specifically, the block interleaver 124 may interleave by writing the plurality of groups on each column of the at least one column in group units in a column direction, and reading each row of the at least one column in which the plurality of groups are written in group units in a row direction.

Hereinafter, the group located in the j^th position after being interleaved by the group interleaver 122 will be referred to as group Y_j.

When the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves the plurality of groups by writing as many groups as the number of groups divided by the number of columns in each column serially in group units.

For example, as shown in FIG. 8, the block interleaver 124 writes bits included in group Y₀, group Y₁, . . . , group Y_p−1 in the 1^st column from the 1^st row to the R₁^th row, writes bits included in group Y_p, group Y_p+1, . . . , group Y_q-1 in the 2nd column from the 1^st row to the R₁th row, . . . , and writes bits included in group Y_z, Y_z+1, . . . , group Y_Ngroup-1 in the column C from the 1^st row to the R₁^th row. The block interleaver 124 may read each row of the plurality of columns in a row direction from the 1^st row. Each column may include rows from 1 to R₁. That is, each column is formed of R₁ number of rows.

However, when the number of groups of the LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 may interleave by dividing each column into N number of parts (N is an integer greater than or equal to 2).

Specifically, the block interleaver 124 divides each column into a part including as many rows as the number of bits included in groups which can be written in each column in group units, and a part including the other rows, and interleaves the plurality of groups by using the divided parts.

The part including as many rows as the number of bits included in the groups which can be written in group units is formed of as many rows as an integer multiple of M. In addition, as described above, the number of codeword bits forming each group may be a divisor of M and thus, a part including columns as many as the number of bits included in each group which can be written by group units may consist of rows as many as the integer multiple of the number of bits forming each group.

In this case, the block interleaver 124 writes at least some groups which can be written in each of the plurality of columns in group units from among the plurality of groups in each of the plurality of columns serially, and then writes the other groups in the other area which remains after the at least some groups have been written in group units in each of the plurality of columns. That is, the block interleaver 124 writes the bits included in the at least some writeable group in the first part (that is, part 1) of each column in group units, and then divides the bits included in the other groups and writes the bits in the second part (that is, part 2) of each column.

For example, it is assumed that the block interleaver 124 divides each column into the first part including R₁ number of rows and the second part including R₂ number of rows as shown in FIGS. 9 and 10. Herein, R₁ corresponds to the number of bits included in the groups which can be written in each column in group units, and R₂ is R₁ subtracted from the total number of rows of each column.

In this case, the block interleaver 124 writes the bits included in the groups which can be written in each column in group units in the first part of each column in the column direction.

That is, as shown in FIGS. 9 and 10, the block interleaver 124 writes the bits included in each of group Y₀, group Y₁, . . . , group Y_n−1 in the 1^st to R₁^th rows of the first part of the 1^st column, writes bits included in each of group Y_n, group Y_n+1, . . . , group Y_m-1 in the 1^st to R₁^th rows of the first part of the 2^nd column, . . . , writes bits included in each of group Y_e, group Y_e+1, . . . , group Y_Ngroup-2 in the 1^st to R₁^th rows of the first part of the column C.

As described above, the block interleaver 124 writes the bits included in the groups which can be written in each column in group units in the first part of each column in the column direction.

Thereafter, the block interleaver 124 divides bits included in the other groups except the groups written in the first part of each column from among the plurality of groups, and writes the bits in the second part of each column in the column direction. In this case, the block interleaver 124 divides the bits included in the other groups except the groups written in the first part of each column by the number of columns, so that the same number of bits are written in the second part of each column, and writes the divided bits in the second part of each column in the column direction.

For example, when the last group Y_Ngroup-1 of the LDPC codeword remains as shown in FIG. 9, the block interleaver 124 divides the bits included in the group Y_Ngroup-1 by the number of columns (C), and writes the divided bits in the second part of each column serially.

That is, the block interleaver 124 writes the bits in the 1^st to R₂^th rows of the second part of the 1^st column, writes the bits in the 1^st to R₂^th rows of the second part of the 2nd column, . . . , etc., and writes the bits in the 1^st to R₂^th rows of the second part of the column C. In this case, the block interleaver 124 may write the bits in the second part of each column in the column direction as shown in FIG. 9. In other words, the bits forming a bit group in the second part may be written not in the same rows but in a plurality of rows.

In the above-described example, the block interleaver 124 writes the bits in the second part in the column direction. However, this is merely an example. That is, the block interleaver 124 may write the bits in the plurality of columns of the second parts in a row direction. In this case, the block interleaver 124 may write the bits in the first part in the same method as described above.

Specifically, referring to FIG. 10, the block interleaver 124 writes the bits from the 1^st row of the second part in the 1^st column to the 1^st row of the second part in the column C, writes the bits from the 2^nd row of the second part in the 1^st column to the 2^nd row of the second part in the column C, . . . , etc., and writes the bits from the R₂^th row of the second part in the 1^st column to the R₂^th row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written in each row of each part in the row direction. That is, as shown in FIGS. 9 and 10, the block interleaver 124 reads the bits written in each row of the first part of the plurality of columns serially in the row direction, and reads the bits written in each row of the second part of the plurality of columns serially in the row direction.

As described above, the block interleaver 124 may interleave the plurality of groups in the methods described above with reference to FIGS. 8 to 10.

In particular, in the case of FIG. 9, the bits included in the group which does not belong to the first part are written in the second part in the column direction and read in the row direction. In view of this, the order of the bits included in the group which does not belong to the first part is rearranged. Since the bits included in the group which does not belong to the first part are interleaved as described above, Bit Error Rate (BER)/Frame Error Rate (FER) performance can be improved in comparison with a case in which such bits are not interleaved.

However, the group which does not belong to the first part may not be interleaved as shown in FIG. 10. That is, since the block interleaver 124 writes and read the bits included in the group which does not belong to the first part on and from the second part in the row direction, the order of the bits included in the group which does not belong to the first part is not changed and the bits are output to the modulator 130 serially. In this case, the bits included in the group which does not belong to the first part may be output serially and mapped onto a modulation symbol.

In FIGS. 9 and 10, the last single group of the plurality of groups is written in the second part. However, this is merely an example. The number of groups written in the second part may vary according to the total number of groups of the LDPC codeword, the number of columns and rows or the number of transmit antenna.

The block interleaver 124 may have a different configuration according to whether bits included in a same group are mapped onto a single bit of each modulation symbol or bits included in a same group are mapped onto two bits of each modulation symbol.

Meanwhile, in case of a system where the block interleaver 124 uses a plurality of antennas, the block interleaver 124 may determine the number of columns in consideration of the number of bits forming a modulation symbol and the number of antennas in use simultaneously. For example, in a case where a plurality of bits included in the same group are respectively mapped onto a single bit of each modulation symbol, and two antennas are used, the block interleaver 124 may determine the number of columns as twice the number of bits forming a modulation symbol.

First, when bits included in the same group are mapped onto a single bit of each modulation symbol, the block interleaver 124 may have configurations as shown in Tables 57 and 58:

	TABLE 57
	Nldpc = 64800
				256
	QPSK	16 QAM	64 QAM	QAM	1024 QAM	4096 QAM
C	2	4	6	8	10	12
R1	32400	16200	10800	7920	6480	5400
R2	0	0	0	180	0	0

	TABLE 58
	Nldpc = 16200
				256
	QPSK	16 QAM	64 QAM	QAM	1024 QAM	4096 QAM
C	2	4	6	8	10	12
R1	7920	3960	2520	1800	1440	1080
R2	180	90	180	225	180	270

Herein, C (or NO is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ is the number of rows constituting the second part in each column.

Referring to Tables 57 and 58, when the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to the number of bits constituting a modulation symbol, bits included in a same group are mapped onto a single bit of each modulation symbol as shown in Tables 57 and 58.

For example, when N_ldpc=64800 and the modulation method is 16-QAM, the block interleaver 124 may use four (4) columns each including 16200 rows. In this case, a plurality of groups of an LDPC codeword are written in the four (4) columns in group units and bits written in the same row in each column are output serially. In this case, since four (4) bits constitute a single modulation symbol in the modulation method of 16-QAM, bits included in the same group and output from a single column may be mapped onto a single bit of each modulation symbol. For example, bits included in a group written in the 1^st column may be mapped onto the first bit of each modulation symbol.

On the other hand, when bits included in a same group are mapped onto two bits of each modulation symbol, the block interleaver 124 may have configurations as shown in Tables 59 and 60:

	TABLE 59
	Nldpc = 64800
						4096
	QPSK	16 QAM	64 QAM	256 QAM	1024 QAM	QAM
C	1	2	3	4	5	6
R1	64800	32400	21600	16200	12960	10800
R2	0	0	0	0	0	0

	TABLE 60
	Nldpc = 16200
					1024	4096
	QPSK	16 QAM	64 QAM	256 QAM	QAM	QAM
C	1	2	3	4	5	6
R1	16200	7920	5400	3960	3240	2520
R2	0	180	0	0	0	180

Herein, C (or NO is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ is the number of rows constituting the second part in each column.

Referring to Tables 59 and 60, when the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is half of the number of bits constituting a modulation symbol as shown in Tables 59 and 60, bits included in a same group are mapped onto two bits of each modulation symbol.

For example, when N_ldpc=64800 and the modulation method is 16-QAM, the block interleaver 124 may use two (2) columns each including 32400 rows. In this case, a plurality of groups of an LDPC codeword are written in the two (2) columns in group units and bits written in the same row in each column are output serially. Since four (4) bits constitute a single modulation symbol in the modulation method of 16-QAM, bits output from two rows constitute a single modulation symbol. Accordingly, bits included in the same group and output from a single column may be mapped onto two bits of each modulation symbol. For example, bits included in a group written in the 1^st column may be mapped onto bits existing in any two positions of each modulation symbol.

Referring to Tables 57 to 60, the total number of rows of the block interleaver 124, that is, R₁+R₂, is N_ldpc/C.

In addition, the number of rows of the first part, R₁, is an integer multiple of the number of bits included in each group, M (e.g., M=360), and maybe expressed as └N_group/C ┘×M, and the number of rows of the second part, R₂, may be N_ldpc/C−R₁. Herein, └N_group/C┘ is the largest integer below N_ldpc/C. Since R₁ is an integer multiple of the number of bits included in each group, M, bits may be written in R₁ in group units.

In addition, when the number of groups of an LDPC codeword is not an integer multiple of the number of columns, it can be seen from Tables 57 to 60 that the block interleaver 124 interleaves a plurality of groups of the LDPC codeword by dividing each column into two parts.

Specifically, the length of an LDPC codeword divided by the number of columns is the total number of rows included in the each column. In this case, when the number of groups of the LDPC codeword is an integer multiple of the number of columns, each column is not divided into two parts. However, when the number of groups of the LDPC codeword is not an integer multiple of the number of columns, each column is divided into two parts.

For example, it is assumed that the number of columns of the block interleaver 124 is identical to the number of bits constituting a modulation symbol, and an LDPC codeword is formed of 64800 bits as shown in Table 57. In this case, the LDPC codeword is formed of 64800/360(=180) groups.

When the modulation method is 16-QAM, each column may have 64800/4(=16200) rows. In this case, since the number of groups of an LDPC codeword divided by the number of columns is 180/4(=45), bits can be written in each column in group units without dividing each column into two parts. That is, bits included in 45 groups, that is, 45×360(=16200) bits can be written in each column.

However, when the modulation method is 256-QAM, each column may have 64800/8(=8100) rows. In this case, since the number of groups of an LDPC codeword divided by the number of columns is 180/8=22.5, each column is divided into two parts.

In this case, since the bits should be written in the first part of each column in group units, the first part of each column has 22×360(=7920) rows and 7920 bits included in 22 groups may be written. The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 8100-7920(=180) rows, and 180 bits can be written. In this case, the bits included in the other group which has not been written in the first part are divided and written in the second part of each column.

In another example, it is assumed that the number of columns of the block interleaver 124 is half of the number of bits constituting the modulation symbol, and the LDPC codeword is formed of 16200 bits as shown in Table 60. In this case, the LDPC codeword is formed of 16200/360(=45) groups.

When the modulation method is 64-QAM, each column may have 16200/3(=5400) rows. In this case, since the number of groups of the LDPC codeword divided by the number of columns is 45/3(=15), bits can be written in each column in group units without dividing each column into two parts. That is, bits included in the 15 groups, that is, 15×360(=5400) bits can be written in each column.

However, when the modulation method is 256-QAM, each column may have 16200/4(=4050) rows. In this case, since the number of groups of the LDPC codeword divided by the number of columns is 45/4=11.25, each column is divided into 2 parts.

In this case, since the bits should be written in the first part of each column in group units, the first part of each column has 11×360(=3960) rows and 3960 bits included in 11 groups may be written. The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 4050-3960(=90) rows, and 90 bits can be written. In this case, the bits included in the other group which has not been written in the first part are divided and written in the second part of each column.

Hereinafter, the block interleaver of FIG. 4 according to an exemplary embodiment will be explained in detail with reference to FIG. 11.

In a group-interleaved LDPC codeword (v₀, v₁, . . . , v_Nldpc−1), Y_j is continuously arranged like V={Y₀, Y₁, . . . Y_Ngroup−1}.

The LDPC codeword after group interleaving may be interleaved by the block interleaver 124 as shown in FIG. 11. Specifically, an input bit v_i is written from the first part to the second part serially in a column direction, and is read from the first part to the second part serially in a row direction.

In this case, the number of columns and the number of rows of the first part and the second part of the block interleaver 124 vary according to a modulation method as in Table 61 presented below.

Herein, a sum of the number of rows of the first part, N_r1 and the number of rows of the second part, N_r2, is equal to N_ldpc/N_C (herein, N_C is the number of columns). In addition, since N_r1 is a multiple of 360, a plurality of bit groups may be written in the first part.

TABLE 61
	Rows in Part 1 Nr1	Rows in Part 2 Nr2
	Nldpc =	Nldpc =	Nldpc =	Nldpc =	Columns
Modulation	64800	16200	64800	16200	Nc
16-QAM	16200	3960	0	90	4
64-QAM	10800	2520	0	180	6
256-QAM	7920	1800	180	225	8
1024-QAM	6480	1440	0	180	10

Hereinafter, an operation of the block interleaver 124 will be explained in detail.

Specifically, as shown in FIG. 11, the input bit v_i (0≦i<N_C×N_r1) is written in r_i row of c_i column of the first part of the block interleaver 124. Herein, c_i and r₁ are

$c_i\lfloor \frac{i}{N_{r1}}\rfloor$

and r_i=(i mod N_r1), respectively.

In addition, the input bit v_i (N_C×N_r1≦i<N_ldpc) is written in an r_i row of c_i column of the second part of the block interleaver 124. Herein, c_i and r_i are

$c_i\lfloor \frac{\left(i-N_cN_{r1}\right)}{N_{r2}}\rfloor$

and r_i=N_r1+{(i−N_C×N_r1) mod N_r2}, respectively.

An output bit q_j(0≦j<N_ldpc) is read from c_j column of r_j row. Herein, r_j and c_j are

$r_j\lfloor \frac{j}{N_c}\rfloor$

and c_j=0 mod NO, respectively.

For example, when the length N_ldpc of an LDPC codeword is 64800 and the modulation method is 256-QAM, an order of bits output from the block interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈, q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . . , v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, . . . , v₆₄₇₉₉). Herein, the indexes of the right side of the foregoing equation may be specifically expressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680, 39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441, . . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360, 63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719, 63899, 64079, 64259, 64439, 64619, 64799.

Referring back to FIG. 1, the modulator 130 maps an interleaved LDPC codeword onto modulation symbols. Specifically, the modulator 130 may demultiplex the interleaved LDPC codeword and modulate the demultiplexed LDPC codeword and map it onto a constellation.

First, the modulator 130 demultiplexes the interleaved LDPC codeword. To achieve this, the modulator 130 may include a demultiplexer shown in FIG. 12 or 13 to demultiplex the interleaved LDPC codeword.

The demultiplexer demultiplexes the interleaved LDPC codeword. Specifically, the demultiplexer performs serial-to-parallel conversion with respect to the interleaved LDPC codeword, and demultiplexes the interleaved LDPC codeword into a cell having a predetermined number of bits (or a data cell).

For example, as shown in FIG. 12, the demultiplexer receives the LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from the interleaver 120, outputs the received LDPC codeword bits to one of a plurality of substreams serially, converts the input LDPC codeword bits into cells, and outputs the cells.

Herein, the number of substreams, N_substreams, may be equal to the number of bits constituting a modulation symbol, η_mod, and the number of bits constituting the cell may be equal to N_ldpc/η_mod. η_mod varies according to a modulation method and the number of generated cells varies according to the length N_ldpc of the LDPC codeword as in Table 62 presented below:

TABLE 62
		Number of output	Number of output
Modulation		data cells for	data cells for
mode	ηMOD	Nldpc = 64 800	Nldpc = 16 200
QPSK	2	32 400	8 100
16-QAM	4	16 200	4 050
64-QAM	6	10 800	2 700
256-QAM	8	8 100	2 025
1024-QAM	10	6 480	1 620

Bits having the same index in each of the plurality of sub-streams may constitute a same cell. That is, in FIG. 12, each cell may be expressed as (y_0,0, y_1,0, . . . , y_ηMOD−1,0), (y_0,1, y_1,1, . . . , y_ηMOD−1,1).

The demultiplexer may demultiplex an input LDPC codeword bits in various methods. That is, the demultiplexer may change an order of the LDPC codeword bits and output the bits to each of the plurality of substreams, or may output the bits to each of the plurality of streams serially without changing the order of the LDPC codeword bits. These operations may be determined according to the number of columns used for interleaving in the block interleaver 124.

Specifically, when the block interleaver 124 includes as many columns as half of the number of bits constituting a modulation symbol, the demultiplexer may change the order of the input LDPC codeword bits and output the bits to each of the plurality of sub-streams. An example of a method for changing the order is illustrated in Table 63 presented below:

	TABLE 63
	Modulation format	QPSK
	Input bit	0	1
	di mod Nsubstreams
	output bit-number	0	1
	Modulation format	16 QAM
	Input bit	0	1	2	3
	di mod Nsubstreams
	output bit-number	0	2	1	3
	Modulation format	64 QAM
	Input bit	0	1	2	3	4	5
	di mod Nsubstreams
	output bit-number	0	3	1	4	2	5
Modulation format	255 QAM
Input bit	0	1	2	3	4	5	6	7
di mod Nsubstreams
output bit-number	0	4	1	5	2	6	3	7
Modulation format	1024 QAM
Input bit	0	1	2	3	4	5	6	7	8	9
di mod Nsubstreams
output bit-number	0	5	1	6	2	7	3	5	4	9
Modulation
format	4095 QAM
Input bit	0	1	2	3	4	5	6	7	8	9	10	11
di mod
Nsubstreams
output bit-	0	6	1	7	2	8	3	9	4	10	5	11
number
indicates data missing or illegible when filed

According to Table 63, when the modulation method is 16-QAM for example, the number of substreams is four (4) since the number of bits constituting the modulation symbol is four (4) in the case of 16-QAM. In this case, the demultiplexer may output, from among the serially input bits, bits with an index i satisfying i mod 4=0 to the 0^th substream, bits with an index i satisfying i mod 4=1 to the 2^nd substream, bits with an index i satisfying i mode 4=2 to the 1^st substream, and bits with an index i satisfying i mode 4=3 to the 3^rd substream.

Accordingly, the LDPC codeword bits input to the demultiplexer, (q₀, q₁, q₂, . . . ), may be output as cells like (y_0,0, y_1,0, y_2,0, y_3,0)=(q₀, q₂, q₁, q₃), (y_0,1, y_1,1, y_2,1, y_3,1)=(q₄, q₆, q₅, q₇), . . . .

When the block interleaver 124 includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer may output the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. That is, as shown in FIG. 13, the demultiplexer may output the input LDPC codeword bits (q₀, q₁, q₂, . . . ) to each of the substreams serially, and accordingly, each cell may be configured as (y_0,0, y_1,0, . . . , y_ηMOD−1,0)=(q₀, q₁, . . . , q_ηMOD−1), (y_0,1, y_1,1, . . . , y_ηMOD−1,1)=(q_ηMOD, q_ηMOD+1, . . . , q_2×ηMOD−1), . . . .

In the above-described example, the demultiplexer outputs the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. However, this is merely an example. That is, according to an exemplary embodiment, when the block interleaver 124 includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer may be omitted.

The modulator 130 may map the demultiplexed LDPC codeword onto modulation symbols. However, when the demultiplexer is omitted as described above, the modulator 130 may map LDPC codeword bits output from the interleaver 120, that is, block-interleaved LDPC codeword bits, onto modulation symbols.

The modulator 130 may modulate bits (that is, cells) output from a demultiplexer in various modulation methods such as QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, 4096-QAM, etc. When the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM and 4096-QAM, the number of bits constituting a modulation symbol, η_MOD (that is, a modulation degree), may be 2, 4, 6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer is formed of as many bits as the number of bits constituting a modulation symbol, the modulator 130 may generate a modulation symbol by mapping each cell output from the demultiplexer onto a constellation point serially. Herein, a modulation symbol corresponds to a constellation point on the constellation.

However, when the demultiplexer is omitted, the modulator 130 may generate modulation symbols by grouping a predetermined number of bits from interleaved bits sequentially and mapping the predetermined number of bits onto constellation points. In this case, the modulator 130 may generate the modulation symbols by using η_MOD number of bits sequentially according to a modulation method.

The modulator 130 may modulate by mapping cells output from the demultiplexer onto constellation points in a uniform constellation (UC) method.

The uniform constellation method refers to a method for mapping a modulation symbol onto a constellation point so that a real number component Re(z_q) and an imaginary number component Im(z_q) of a constellation point have symmetry and the modulation symbol is placed at equal intervals. Accordingly, at least two of modulation symbols mapped onto constellation points in the uniform constellation method may have the same demodulation performance.

Examples of the method for generating a modulation symbol in the uniform constellation method according to an exemplary embodiment are illustrated in Tables 64 to 71 presented below, and an example of a case of a uniform constellation 64-QAM is illustrated in FIG. 14.

TABLE 64
	y0, q	1	0
	Re(zq)	−1	1

TABLE 65
	Y1, q	1	0
	Im(zq)	−1	1

TABLE 66
	y0, q	1	1	0	0
	y2, q	0	1	1	0
	Re(zq)	−3	−1	1	3

TABLE 67
	y1, q	1	1	0	0
	y2, q	0	1	1	0
	Im(zq)	−3	−1	1	3

	TABLE 68
	y0,q	1	1	1	1	0	0	0	0
	y2,q	0	0	1	1	1	1	0	0
	y4,q	0	1	1	0	0	1	1	0
	Re(zq)	−7	−5	−3	−1	1	3	5	7

	TABLE 69
	y1,q	1	1	1	1	0	0	0	0
	y3,q	0	0	1	1	1	1	0	0
	y5,q	0	1	1	0	0	1	1	0
	Im(zq)	−7	−5	−3	−1	1	3	5	7

TABLE 70
y0,q	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0
y2,q	0	0	0	0	1	1	1	1	1	1	1	1	0	0	0	0
y4,q	0	0	1	1	1	1	0	0	0	0	1	1	1	1	0	0
Re(zq)	−15	−13	−11	−9	−7	−5	−3	−1	1	3	5	7	9	11	13	15

TABLE 71
y1,q	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0
y3,q	0	0	0	0	1	1	1	1	1	1	1	1	0	0	0	0
y5,q	0	0	1	1	1	1	0	0	0	0	1	1	1	1	0	0
y7,q	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1	0
Im(zq)	−15	−13	−11	−9	−7	−5	−3	−1	1	3	5	7	9	11	13	15

Tables 64 and 65 are used for determining a real number component Re(z_q) and an imaginary number component Im(z_q) when the modulation is performed in a QPSK method, Tables 66 and 67 are used for determining a real number component Re(z_q) and an imaginary number component Im(z_q) when the modulation is performed in a 16-QAM method, Tables 68 and 69 are used for determining a real number component Re(z_q) and an imaginary number component Im(z_q) when the modulation is performed in a 64-QAM method, and Tables 70 and 71 are used for determining a real number component Re(z_q) and an imaginary number component Im(z_q) when the modulation is performed in a 256-QAM method.

Referring to Tables 64 to 71, performance (e.g., reliability) varies according to whether a plurality of bits constituting a modulation symbol correspond to most significant bits (MSBs) or least significant bits (LSBs).

For example, in the case of 16-QAM, from among four (4) bits constituting a modulation symbol, each of the first and second bits determines a sign of each of the real number component Re(z_q) and the imaginary number component Im(z_q) of a constellation point onto which a modulation symbol is mapped, and the third and fourth bits determine a size of the constellation point onto which the modulation symbol is mapped.

In this case, the first and second bits for determining the sign from among the four (4) bits constituting the modulation symbol have a higher reliability than the third and fourth bits for determining the size.

In another example, in the case of 64-QAM, from among six (6) bits constituting a modulation symbol, each of the first and second bits determines a sign of each of the real number component Re(z_q) and the imaginary number component Im(z_q) of a constellation point onto which the modulation symbol is mapped. In addition, the third to sixth bits determine a size of the constellation point onto which the modulation symbol is mapped. From among these bits, the third and fourth bits determine a relatively large size, and the fifth and sixth bits determine a relatively small size (for example, the third bit determines which of sizes (−7, −5) and (−3, −1) corresponds to the constellation point onto which the modulation symbol is mapped, and, when (−7, −5) is determined by the third bit, the fourth bit determines which of −7 and −5 corresponds to the size of the constellation point.).

In this case, the first and second bits for determining the sign from among the six bits constituting the modulation symbol have the highest reliability, and the third and fourth bits for determining the relatively large size has the higher reliability than the fifth and sixth bits for determining the relatively small size.

As described above, in the case of the uniform constellation method, the bits constituting a modulation symbol have different reliability according to mapping locations in the modulation symbol.

The modulator 130 may modulate by mapping cells output from the demultiplexer onto constellation points in a non-uniform constellation (NUC) method.

Specifically, the modulator 130 may modulate bits output from the demultiplexer in various modulation methods such as non-uniform 16-QAM, non-uniform 64-QAM, non-uniform 256-QAM, non-uniform 1024-QAM, non-uniform 4096-QAM, etc.

Hereinafter, a method for generating a modulation symbol by using the non-uniform constellation method according to an exemplary embodiment will be explained.

First, the non-uniform constellation method has the following characteristics:

In the non-uniform constellation method, the constellation points may not regularly be arranged unlike in the uniform constellation method. Accordingly, when the non-uniform constellation method is used, performance for a signal-to-noise ratio (SNR) less than a specific value can be improved and a high SNR gain can be obtained in comparison to the uniform constellation method.

In addition, the characteristics of the constellation may be determined by one or more parameters such as a distance between constellation points. Since the constellation points are regularly distributed in the uniform constellation, the number of parameters for specifying the uniform constellation method may be one (1). However, the number of parameters necessary for specifying the non-uniform constellation method is relatively larger and the number of parameters increases as the constellation (e.g., the number of constellation points) increases.

In the case of the non-uniform constellation method, an x-axis and a y-axis may be designed to be symmetric to each other or may be designed to be asymmetric to each other. When the x-axis and the y-axis are designed to be asymmetric to each other, improved performance can be guaranteed, but decoding complexity may increase.

Hereinafter, an example of a case in which the x-axis and the y-axis are designed to be asymmetric to each other will be explained. In this case, once a constellation point of the first quadrant is defined, locations of constellation points in the other three quadrants may be determined as follows. For example, when a set of constellation points defined for the first quadrant is X, the set becomes −conj(X) in the case of the second quadrant, becomes conj(X) in the case of the third quadrant, and becomes −(X) in the case of the fourth quadrant.

That is, once the first quadrant is defined, the other quadrants may be expressed as follows:

1 Quarter (first quadrant)=X

2 Quarter (second quadrant)=−conj(X)

3 Quarter (third quadrant)=conj(X)

4 Quarter (fourth quadrant)=−X

Specifically, when the non-uniform M-QAM is used, M number of constellation points may be defined as z={z₀, z₁, . . . , z_M-1}. In this case, when the constellation points existing in the first quadrant are defined as {x₀, x₁, x₂, . . . , X_M/4-1}, z may be defined as follows:

from z₀ to z_M/4-1=from x₀ to x_M/4

from z_M/4 to z_2×M/4−1=−conj(from x₀ to x_M/4)

from z_2×M/4 to z_3×M/4-1=conj(from x₀ to x_M/4)

from z_3×M/4 to z_4×M/4-1=−(from x₀ to x_M/4)

Accordingly, the modulator 130 may map the bits [y₀, . . . , y_m-1] output from the demultiplexer onto constellation points in the non-uniform constellation method by mapping the output bits onto z_L having an index of

$L=\sum _{i=0}^{m-1}\left(y_12^{m-1}\right).$

An example of the constellation of the non-uniform constellation method is illustrated in FIGS. 15 to 19.

An example of the method for modulating asymmetrically in the non-uniform constellation method in the modulator 130 is illustrated as in Tables 72 to 77 presented below. That is, according to an exemplary embodiment, modulation is performed in the non-uniform constellation method by defining constellation points existing in the first quadrant and defining constellations points existing in the other quadrants based on Tables 72 to 77.

	TABLE 72
	Shape
x	R6/15	R7/15	R8/15	R9/15	R10/15
x0	0.4530 + 0.2653i	1.2103 + 0.5026i	0.4819 + 0.2575i	0.4509 + 1.2007i	0.2173 + 0.4189i
x1	0.2663 + 0.4530i	0.5014 + 1.2103i	0.2575 + 0.4819i	1.2007 + 0.4909i	0.6578 + 0.2571i
x2	1.2092 + 0.5115i	0.4634 + 0.2624i	1.2068 + 0.4951i	0.2476 + 0.5065i	0.4326 + 1.1445i
x3	0.5115 + 1.7092i	0.2624 + 0.4627i	0.4951 + 1.2068i	0.5053 + 0.2476i	1.2088 + 0.5659i
	Shape
	x	R11/15	R12/15	R13/15
	x0	0.5593 + 0.9547i	0.2999 + 0.2999i	0.9517 + 0.9511i
	x1	0.9547 + 0.2909i	0.9540 + 0.2999i	0.9524 + 0.3061i
	x2	0.2921 + 0.9583i	0.2999 + 0.9540i	0.3067 + 0.9524i
	x3	0.2909 + 0.2927i	0.9540 + 0.9540i	0.3061 + 0.3067i

	TABLE 73
	Shape
x	R64_6/15	R64_7/15	R64_8/15	R64_9/15	R64_10/25
x0	0.4337 + 1.6023i	0.3352 + 0.6028i	1.4827 + 0.2920i	0.3547 + 0.6149i	1.4388 + 0.2878i
x1	1.6023 + 0.4387i	0.2077 + 0.6584i	1.2563 + 0.8411i	0.1581 + 0.0842i	1.2150 + 0.8133i
x2	0.8753 + 1.0881i	0.1711 + 0.3028i	1.0211 + 0.2174i	0.1567 + 0.2749i	1.0386 + 0.2219i
x3	1.0881 + 0.8753i	0.1556 + 0.3035i	0.8798 + 0.5702i	0.1336 + 0.2700i	0.8494 + 0.6145i
x4	0.2202 + 0.9238i	0.6028 + 0.3345i	0.2920 + 1.4827i	0.6177 + 0.4030i	0.2931 + 1.4656i
x5	0.2019 + 0.7818i	0.6577 + 0.2084i	0.8410 + 1.2563i	0.7262 + 0.1756i	0.8230 + 1.2278i
x6	0.3049 + 0.8454i	0.3021 + 0.1711i	0.2174 + 1.0211i	0.3568 + 0.1756i	0.2069 + 1.0649i
x7	0.2653 + 0.7540i	0.3028 + 0.1556i	0.5702 + 0.8758i	0.3771 + 0.1336i	0.5077 + 0.8971i
x8	0.7818 + 0.2019i	0.5556 + 0.8922i	0.3050 + 0.1475i	0.5639 + 0.8864i	0.4119 + 0.1177i
x9	0.9238 + 0.2202i	0.2152 + 1.0190i	0.3028 + 0.1691i	0.1980 + 1.0277i	0.3993 + 0.2516i
x10	0.7540 + 0.2653i	0.8450 + 1.2619i	0.6555 + 0.1871i	0.8199 + 1.2515i	0.7412 + 0.1559i
x11	0.8454 + 0.1049i	0.2922 + 1.4894i	0.6126 + 0.3563i	0.2854 + 1.4691i	0.5954 + 0.4328i
x12	0.2675 + 0.2479i	0.6929 + 0.5549i	0.1475 + 0.3040i	0.8654 + 0.6058i	0.1166 + 0.1678i
x13	0.2479 + 0.2675i	1.0197 + 0.2359i	0.1691 + 0.3028i	1.0382 + 0.2141i	0.1582 + 0.3325i
x14	0.2890 + 0.2701i	1.2626 + 0.8457i	0.1871 + 0.6855i	1.2362 + 0.8416i	0.1355 + 0.7408i
x15	0.2701 + 0.2890i	1.4894 + 0.2922i	0.3563 + 0.0126i	1.4663 + 0.2973i	0.3227 + 0.6200i
	Shape
	x	R64_11/15	R64_12/15	R64_13/15
	x0	0.3317 + 0.6970i	1.0854 + 0.5394i	0.4108 + 0.7473i
	x1	0.1386 + 0.8824i	0.7353 + 0.4623i	0.1343 + 0.5338i
	x2	0.1323 + 0.4437i	1.0474 + 0.1695i	0.1570 + 0.9240i
	x3	0.1015 + 0.1372i	0.7243 + 0.1504i	0.1230 + 0.1605i
	x4	0.5682 + 0.4500i	1.0693 + 0.9408i	0.6285 + 0.4617i
	x5	0.6739 + 0.1435i	0.7092 + 0.8073i	0.3648 + 0.3966i
	x6	0.3597 + 0.3401i	1.4261 + 0.2216i	0.6907 + 0.1541i
	x7	0.3660 + 0.1204i	0.6106 + 1.1783i	0.3995 + 0.1308i
	x8	0.6054 + 0.8922i	0.1392 + 0.4078i	0.7268 + 0.8208i
	x9	0.2120 + 1.2253i	0.4262 + 0.4205i	1.0463 + 0.9495i
	x10	0.9594 + 1.0714i	0.1407 + 0.1336i	0.1866 + 1.2733i
	x11	0.5829 + 1.3995i	0.4265 + 0.1368i	0.5507 + 1.1793i
	x12	0.8439 + 0.5675i	0.1338 + 0.7057i	0.9283 + 0.5140i
	x13	0.9769 + 0.1959i	0.4197 + 0.7206i	1.2648 + 0.5826i
	x14	1.2239 + 0.6760i	0.1682 + 1.0316i	0.9976 + 0.1718i
	x15	1.3653 + 0.2323i	0.2287 + 1.3914i	1.3412 + 0.1944i

	TABLE 74
	Shape
x	NUC_64_6/15	NUC_64_7/15	NUC_64_8/15	NUC_64_9/15	NUC_64_10/15
x0	0.4387 + 1.6023i	0.3352 + 0.6028i	1.4827 + 0.2920i	0.3547 + 0.6149i	1.4388 + 0.2878i
x1	1.6023 + 0.4387i	0.2077 + 0.6584i	1.2563 + 0.8411i	0.1581 + 0.6842i	1.2150 + 0.8133i
x2	0.8753 + 1.0881i	0.1711 + 0.3028i	1.0211 + 0.2174i	0.1567 + 0.2749i	1.0386 + 0.2219i
x3	1.0881 + 0.8753i	0.1556 + 0.3035i	0.8798 + 0.5702i	0.1336 + 0.2700i	0.8494 + 0.6145i
x4	0.2202 + 0.9238i	0.6028 + 0.3345i	0.2920 + 1.4827i	0.6177 + 0.4030i	0.2931 + 1.4656i
x5	0.2019 + 0.7818i	0.6577 + 0.2084i	0.8410 + 1.2563i	0.7262 + 0.1756i	0.8230 + 1.2278i
x6	0.3049 + 0.8454i	0.3021 + 0.1711i	0.2174 + 1.0211i	0.3568 + 0.1756i	0.2069 + 1.0649i
x7	0.2653 + 0.7540i	0.3028 + 0.1556i	0.5702 + 0.8798i	0.3771 + 0.1336i	0.5677 + 0.8971i
x8	0.7818 + 0.2019i	0.5556 + 0.8922i	0.3040 + 0.1475i	0.5639 + 0.8864i	0.4119 + 0.1177i
x9	0.9238 + 0.2202i	0.2352 + 1.0190i	0.3028 + 0.1691i	0.1980 + 1.0277i	0.3998 + 0.2516i
x10	0.7540 + 0.2653i	0.8450 + 1.2619i	0.6855 + 0.1871i	0.8199 + 1.2515i	0.7442 + 0.1559i
x11	0.8454 + 0.3049i	0.2922 + 1.4894i	0.6126 + 0.3563i	0.2854 + 1.4691i	0.5954 + 0.4328i
x12	0.2675 + 0.2479i	0.8929 + 0.5549i	0.1475 + 0.3040i	0.8654 + 0.6058i	0.1166 + 0.1678i
x13	0.2479 + 0.2675i	1.0197 + 0.2359i	0.1691 + 0.3028i	1.0382 + 0.2141i	0.1582 + 0.3325i
x14	0.2890 + 0.2701i	1.2626 + 0.8457i	0.1871 + 0.6855i	1.2362 + 0.8416i	0.1355 + 0.7408i
x15	0.2701 + 0.2890i	1.4894 + 0.2922i	0.3563 + 0.6126i	1.4663 + 0.2973i	0.3227 + 0.6200i
	Shape
	x	NUC_64_11/15	NUC_64_12/15	NUC_64_13/15
	x0	0.3317 + 0.6970i	1.0854 + 0.5394i	0.8624 + 1.1715i
	x1	0.1386 + 0.8824i	0.7353 + 0.4623i	1.1184 + 0.8462i
	x2	0.1323 + 0.4437i	1.0474 + 0.1695i	0.2113 + 1.3843i
	x3	0.1015 + 0.1372i	0.7243 + 0.1504i	0.7635 + 0.7707i
	x4	0.5682 + 0.4500i	1.0693 + 0.9408i	1.1796 + 0.1661i
	x5	0.6739 + 0.1435i	0.7092 + 0.8073i	1.0895 + 0.4882i
	x6	0.3597 + 0.3401i	1.4261 + 0.2216i	0.8101 + 0.1492i
	x7	0.3660 + 0.1204i	0.6106 + 1.1783i	0.7482 + 0.4477i
	x8	0.6004 + 0.8922i	0.1392 + 0.4078i	0.1524 + 0.9943i
	x9	0.2120 + 1.2253i	0.4262 + 0.4205i	0.1482 + 0.6877i
	x10	0.9594 + 1.0714i	0.1407 + 0.1336i	0.4692 + 1.0853i
	x11	0.5829 + 1.3995i	0.4265 + 0.1388i	0.4492 + 0.7353i
	x12	0.8439 + 0.5675i	0.1388 + 0.7057i	0.1578 + 0.1319i
	x13	0.9769 + 0.1959i	0.4197 + 0.7206i	0.1458 + 0.4025i
	x14	1.2239 + 0.6760i	0.1682 + 1.0316i	0.4763 + 0.1407i
	x15	1.3653 + 0.2323i	0.2287 + 1.3914i	0.4411 + 0.4267i

TABLE 75
	X/Shape	7/15	13/15
	x0	0.1543 + 0.3088l	1.4293 + 0.2286l
	x1	0.1719 + 0.3074l	0.6234 + 1.1799l
	x2	0.2021 + 0.6601l	1.0719 + 0.9247l
	x3	0.3396 + 0.6009l	0.6841 + 0.8071l
	x4	0.3080 + 0.1543l	1.0440 + 0.1692l
	x5	0.3069 + 0.1716l	0.7232 + 0.1541l
	x6	0.6607 + 0.2018l	1.0639 + 0.5312l
	x7	0.6011 + 0.3395l	0.7147 + 0.4706l
	x8	0.2936 + 1.4847l	0.2128 + 1.4368l
	x9	0.8412 + 1.2593l	0.1990 + 1.0577l
	x10	0.2321 + 1.0247l	0.1176 + 0.6586l
	x11	0.5629 + 0.8926l	0.3691 + 0.7533l
	x12	1.4850 + 0.2935l	0.1457 + 0.1261l
	x13	1.2599 + 0.8426l	0.4329 + 0.1380l
	x14	1.0247 + 0.2320l	0.1424 + 0.3819l
	x15	0.8925 + 0.5631l	0.4216 + 0.4265l

	TABLE 76
	Shape
x	R6/15	R7/15	R8/15	R9/15	R10/15
x0	0.6800 + 1.6926i	1.2905 + 1.3099i	1.0804 + 1.3788i	1.3231 + 1.1506i	1.6097 + 0.1548i
x1	0.3911 + 1.3645i	1.0504 + 0.9577i	1.0487 + 0.9862i	0.9851 + 1.2311i	1.5549 + 0.4605i
x2	0.2191 + 1.7524i	1.5329 + 0.8935i	1.6464 + 0.7428i	1.1439 + 0.8974i	1.3226 + 0.1290i
x3	0.2274 + 1.4208i	1.1577 + 0.8116i	1.3245 + 0.9414i	0.9343 + 0.9271i	1.2772 + 0.3829i
x4	0.8678 + 1.2487i	1.7881 + 0.2509i	0.7198 + 1.2427i	1.5398 + 0.7962i	1.2753 + 1.0242i
x5	0.7275 + 1.1667i	1.4275 + 0.1400i	0.8106 + 1.0040i	0.9092 + 0.5599i	1.4434 + 0.7540i
x6	0.8747 + 1.0470i	1.4784 + 0.5201i	0.5595 + 1.0317i	1.2222 + 0.6574i	1.0491 + 0.8476i
x7	0.7930 + 1.0406i	1.3408 + 0.4346i	0.6118 + 0.9722i	0.9579 + 0.6373i	1.1861 + 0.6253i
x8	0.2098 + 0.9768i	0.7837 + 0.5867i	1.6768 + 0.2002i	0.7748 + 1.5867i	0.9326 + 0.0970i
x9	0.2241 + 1.0454i	0.8250 + 0.6455i	0.9997 + 0.6844i	0.6876 + 1.2489i	0.8962 + 0.2804i
x10	0.1858 + 0.9878i	0.8256 + 0.5601i	1.4212 + 0.4769i	0.5992 + 0.9208i	1.1044 + 0.1102i
x11	0.1901 + 1.0659i	0.8777 + 0.6110i	1.1479 + 0.6312i	0.6796 + 0.9743i	1.0648 + 0.3267i
x12	0.5547 + 0.8312i	1.0080 + 0.1843i	0.6079 + 0.6566i	0.5836 + 0.5879i	0.7325 + 0.6071i
x13	0.5479 + 0.8651i	1.0759 + 0.1721i	0.7284 + 0.6957i	0.6915 + 0.5769i	0.8260 + 0.4559i
x14	0.6073 + 0.8182i	1.0056 + 0.2758i	0.5724 + 0.7031i	0.5858 + 0.7058i	0.8744 + 0.7153i
x15	0.5955 + 0.8420i	1.0662 + 0.2964i	0.6302 + 0.7259i	0.6868 + 0.6793i	0.9882 + 0.5300i
x16	1.4070 + 0.1790i	0.8334 + 1.5554i	0.1457 + 1.4010i	1.6118 + 0.1497i	0.1646 + 1.6407i
x17	1.7227 + 0.2900i	0.8165 + 1.1092i	0.1866 + 1.7346i	0.9511 + 0.1140i	0.4867 + 1.5743i
x18	1.3246 + 0.2562i	0.6092 + 1.2729i	0.1174 + 1.1035i	1.2970 + 0.1234i	0.1363 + 1.3579i
x19	1.3636 + 0.3654i	0.6728 + 1.1456i	0.1095 + 1.0132i	1.0266 + 0.1191i	0.4023 + 1.3026i
x20	1.3708 + 1.2834i	0.3061 + 1.7469i	0.4357 + 1.3636i	1.5831 + 0.4496i	1.0542 + 1.2584i
x21	1.6701 + 0.8403i	0.1327 + 1.4056i	0.5853 + 1.6820i	0.9328 + 0.3586i	0.7875 + 1.4450i
x22	1.1614 + 0.7909i	0.3522 + 1.3414i	0.3439 + 1.0689i	1.2796 + 0.3894i	0.8687 + 1.0407i
x23	1.2241 + 0.7367i	0.2273 + 1.3081i	0.3234 + 0.9962i	1.0188 + 0.3447i	0.6502 + 1.1951i
x24	0.9769 + 0.1863i	0.5007 + 0.8098i	0.1092 + 0.6174i	0.5940 + 0.1059i	0.0982 + 0.9745i
x25	0.9452 + 0.2057i	0.5528 + 0.8347i	0.1074 + 0.6307i	0.7215 + 0.1100i	0.2842 + 0.9344i
x26	1.0100 + 0.2182i	0.4843 + 0.8486i	0.1109 + 0.6996i	0.5863 + 0.1138i	0.1142 + 1.1448i
x27	0.9795 + 0.2417i	0.5304 + 0.8759i	0.1076 + 0.7345i	0.6909 + 0.1166i	0.3385 + 1.0973i
x28	0.8241 + 0.4856i	0.1715 + 0.9147i	0.3291 + 0.6264i	0.5843 + 0.3604i	0.6062 + 0.7465i
x29	0.8232 + 0.4837i	0.1540 + 0.9510i	0.3126 + 0.6373i	0.6970 + 0.3592i	0.4607 + 0.8538i
x30	0.8799 + 0.5391i	0.1964 + 0.9438i	0.3392 + 0.6999i	0.5808 + 0.3250i	0.7263 + 0.8764i
x31	0.8796 + 0.5356i	0.1788 + 0.9832i	0.3202 + 0.7282i	0.6678 + 0.3290i	0.5450 + 1.0067i
x32	0.1376 + 0.3342i	0.3752 + 0.1667i	0.9652 + 0.1066i	0.1406 + 1.6182i	0.2655 + 0.0746i
x33	0.1383 + 0.3292i	0.3734 + 0.1667i	0.9075 + 0.1666i	0.1272 + 1.2984i	0.2664 + 0.0759i
x34	0.1363 + 0.3322i	0.3758 + 0.1661i	0.9724 + 0.1171i	0.1211 + 0.9644i	0.4571 + 0.0852i
x35	0.1370 + 0.3273i	0.3746 + 0.1649i	0.9186 + 0.1752i	0.1220 + 1.0393i	0.4516 + 0.1062i
x36	0.1655 + 0.3265i	0.4013 + 0.1230i	0.6342 + 0.1372i	0.1124 + 0.6101i	0.2559 + 0.1790i
x37	0.1656 + 0.3227i	0.4001 + 0.1230i	0.6550 + 0.1495i	0.1177 + 0.6041i	0.2586 + 0.1772i
x38	0.1634 + 0.3246i	0.4037 + 0.1230i	0.6290 + 0.1393i	0.1136 + 0.7455i	0.3592 + 0.2811i
x39	0.1636 + 0.3208i	0.4019 + 0.1218i	0.6494 + 0.1504i	0.1185 + 0.7160i	0.3728 + 0.2654i
x40	0.1779 + 0.6841i	0.6025 + 0.3934i	1.3127 + 0.1240i	0.4324 + 1.5679i	0.7706 + 0.0922i
x41	0.1828 + 0.6845i	0.5946 + 0.3928i	0.9572 + 0.4344i	0.3984 + 1.2825i	0.7407 + 0.2260i
x42	0.1745 + 0.6828i	0.6116 + 0.3879i	1.2403 + 0.2631i	0.3766 + 0.9534i	0.6180 + 0.0927i
x43	0.1793 + 0.6829i	0.6019 + 0.3837i	1.0254 + 0.4130i	0.3668 + 1.0301i	0.6019 + 0.1658i
x44	0.3547 + 0.6009i	0.7377 + 0.1618i	0.6096 + 0.4214i	0.3667 + 0.5995i	0.6007 + 0.4980i
x45	0.3593 + 0.6011i	0.7298 + 0.1582i	0.6773 + 0.4284i	0.3328 + 0.5960i	0.6673 + 0.3928i
x46	0.3576 + 0.5990i	0.7274 + 0.1782i	0.5995 + 0.4102i	0.3687 + 0.7194i	0.4786 + 0.3935i
x47	0.3624 + 0.5994i	0.7165 + 0.1746i	0.6531 + 0.4101i	0.3373 + 0.6964i	0.5176 + 0.3391i
x48	0.2697 + 0.1443i	0.1509 + 0.2425i	0.1250 + 0.1153i	0.1065 + 0.1146i	0.0757 + 0.1003i
x49	0.2704 + 0.1433i	0.1503 + 0.2400i	0.1252 + 0.1158i	0.1145 + 0.1108i	0.0753 + 0.1004i
x50	0.2644 + 0.1442i	0.1515 + 0.2437i	0.1245 + 0.1152i	0.1053 + 0.1274i	0.0777 + 0.4788i
x51	0.2650 + 0.1432i	0.1503 + 0.2425i	0.1247 + 0.1156i	0.1134 + 0.1236i	0.0867 + 0.4754i
x52	0.2763 + 0.1638i	0.1285 + 0.2388i	0.3768 + 0.1244i	0.1111 + 0.3821i	0.1023 + 0.2243i
x53	0.2768 + 0.1626i	0.1279 + 0.2419i	0.3707 + 0.1237i	0.1186 + 0.3867i	0.1010 + 0.2242i
x54	0.2715 + 0.1630i	0.1279 + 0.2431i	0.3779 + 0.1260i	0.1080 + 0.3431i	0.1950 + 0.3919i
x55	0.2719 + 0.1618i	0.1279 + 0.2406i	0.3717 + 0.1252i	0.1177 + 0.3459i	0.1881 + 0.3969i
x56	0.6488 + 0.1696i	0.3394 + 0.5764i	0.1161 + 0.3693i	0.3644 + 0.1080i	0.0930 + 0.8122i
x57	0.6462 + 0.1706i	0.3364 + 0.5722i	0.1157 + 0.3645i	0.3262 + 0.1104i	0.2215 + 0.7840i
x58	0.6456 + 0.1745i	0.3328 + 0.5758i	0.1176 + 0.3469i	0.3681 + 0.1173i	0.0937 + 0.6514i
x59	0.6431 + 0.1753i	0.3303 + 0.5698i	0.1171 + 0.3424i	0.3289 + 0.1196i	0.1540 + 0.6366i
x60	0.5854 + 0.3186i	0.1491 + 0.6316i	0.3530 + 0.3899i	0.3665 + 0.3758i	0.4810 + 0.6306i
x61	0.5862 + 0.3167i	0.1461 + 0.6280i	0.3422 + 0.3808i	0.3310 + 0.3795i	0.3856 + 0.7037i
x62	0.5864 + 0.3275i	0.1509 + 0.6280i	0.3614 + 0.3755i	0.3672 + 0.3353i	0.3527 + 0.5230i
x63	0.5873 + 0.3254i	0.1473 + 0.6225i	0.3509 + 0.3656i	0.3336 + 0.3402i	0.3100 + 0.5559i
	Shape
	x	R11/15	R12/15	R13/15
	x0	0.3105 + 0.3382i	1.1014 + 1.1670i	0.3556 + 0.3497i
	x1	0.4342 + 0.3360i	0.8557 + 1.2421i	0.3579 + 0.4945i
	x2	0.3149 + 0.4829i	1.2957 + 0.8039i	0.5049 + 0.3571i
	x3	0.4400 + 0.4807i	1.0881 + 0.8956i	0.5056 + 0.5063i
	x4	0.1811 + 0.3375i	0.5795 + 1.2110i	0.2123 + 0.3497i
	x5	0.0633 + 0.3404i	0.6637 + 1.4215i	0.2116 + 0.4900i
	x6	0.1818 + 0.4851i	0.6930 + 1.0082i	0.0713 + 0.3489i
	x7	0.0633 + 0.4815i	0.8849 + 0.9647i	0.0690 + 0.4960i
	x8	0.3084 + 0.1971i	1.2063 + 0.5115i	0.3527 + 0.2086i
	x9	0.4356 + 0.1993i	1.0059 + 0.4952i	0.3497 + 0.0713i
	x10	0.3098 + 0.0676i	1.4171 + 0.5901i	0.4960 + 0.2123i
	x11	0.4342 + 0.0691i	1.0466 + 0.6935i	0.4974 + 0.0698i
	x12	0.1775 + 0.1985i	0.6639 + 0.6286i	0.2086 + 0.2079i
	x13	0.0640 + 0.1978i	0.8353 + 0.5851i	0.2094 + 0.0690i
	x14	0.1775 + 0.0676i	0.6879 + 0.8022i	0.0676 + 0.2079i
	x15	0.0647 + 0.0669i	0.8634 + 0.7622i	0.0698 + 0.0683i
	x16	0.7455 + 0.3411i	0.1213 + 1.4366i	0.3586 + 0.7959i
	x17	0.5811 + 0.3396i	0.1077 + 1.2098i	0.3571 + 0.6392i
	x18	0.7556 + 0.4669i	0.0651 + 0.9801i	0.5034 + 0.8271i
	x19	0.5862 + 0.4756i	0.2009 + 1.0115i	0.5063 + 0.6600i
	x20	0.9556 + 0.3280i	0.3764 + 1.4264i	0.2146 + 0.7862i
	x21	1.1767 + 0.3091i	0.3237 + 1.2130i	0.2109 + 0.6340i
	x22	0.9673 + 0.4720i	0.5205 + 0.9814i	0.0713 + 0.8093i
	x23	1.2051 + 0.5135i	0.3615 + 1.0163i	0.0698 + 0.6467i
	x24	0.7367 + 0.2015i	0.0715 + 0.6596i	0.2799 + 1.0862i
	x25	0.5811 + 0.2015i	0.2116 + 0.6597i	0.2806 + 1.2755i
	x26	0.7316 + 0.0669i	0.0729 + 0.8131i	0.4328 + 0.9904i
	x27	0.5782 + 0.0669i	0.2158 + 0.8246i	0.4551 + 1.1812i
	x28	0.9062 + 0.1971i	0.5036 + 0.6467i	0.2309 + 0.9414i
	x29	1.2829 + 0.1185i	0.3526 + 0.6572i	0.1077 + 1.3891i
	x30	0.9156 + 0.0735i	0.5185 + 0.8086i	0.0772 + 0.9852i
	x31	1.1011 + 0.0735i	0.3593 + 0.8245i	0.0802 + 1.1753i
	x32	0.3244 + 0.8044i	1.2545 + 0.1010i	0.8301 + 0.3727i
	x33	0.4589 + 0.8218i	1.0676 + 0.0956i	0.8256 + 0.5256i
	x34	0.3207 + 0.6415i	1.4782 + 0.1167i	0.6593 + 0.3668i
	x35	0.4509 + 0.6371i	0.8981 + 0.0882i	0.6623 + 0.5182i
	x36	0.1920 + 0.8196i	0.5518 + 0.0690i	1.0186 + 0.3645i
	x37	0.0633 + 0.8167i	0.6903 + 0.0552i	1.0001 + 0.5242i
	x38	0.1811 + 0.6371i	0.5742 + 0.1987i	1.1857 + 0.2725i
	x39	0.0640 + 0.6415i	0.7374 + 0.1564i	1.3928 + 0.3408i
	x40	0.3331 + 1.0669i	1.2378 + 0.3049i	0.8011 + 0.2227i
	x41	0.4655 + 1.0087i	1.0518 + 0.3032i	0.7981 + 0.0735i
	x42	0.3433 + 1.2865i	1.4584 + 0.3511i	0.6459 + 0.2198i
	x43	0.5004 + 1.5062i	0.9107 + 0.2603i	0.6430 + 0.0713i
	x44	0.1971 + 1.0051i	0.6321 + 0.4729i	0.9681 + 0.2205i
	x45	0.0735 + 1.0298i	0.7880 + 0.4392i	0.9615 + 0.0735i
	x46	0.1498 + 1.5018i	0.6045 + 0.3274i	1.3327 + 0.1039i
	x47	0.0865 + 1.2553i	0.7629 + 0.2965i	1.1359 + 0.0809i
	x48	0.7811 + 0.8080i	0.0596 + 0.0739i	0.8382 + 0.8709i
	x49	0.6167 + 0.8153i	0.1767 + 0.0731i	0.8145 + 0.6934i
	x50	0.7636 + 0.6255i	0.0612 + 0.2198i	0.6645 + 0.8486i
	x51	0.6000 + 0.6327i	0.1815 + 0.2192i	0.6600 + 0.6786i
	x52	0.9898 + 0.7680i	0.4218 + 0.0715i	1.1612 + 0.6949i
	x53	1.5855 + 0.1498i	0.2978 + 0.0725i	0.9785 + 0.6942i
	x54	0.9476 + 0.6175i	0.4337 + 0.2115i	1.3698 + 0.6259i
	x55	1.4625 + 0.4015i	0.3057 + 0.2167i	1.2183 + 0.4841i
	x56	0.8276 + 1.0225i	0.0667 + 0.5124i	0.7989 + 1.0498i
	x57	0.6313 + 1.0364i	0.2008 + 0.5095i	0.4395 + 1.4203i
	x58	0.8815 + 1.2865i	0.0625 + 0.3658i	0.6118 + 1.0246i
	x59	0.6342 + 1.2705i	0.1899 + 0.3642i	0.6303 + 1.2421i
	x60	1.0422 + 0.9593i	0.4818 + 0.4946i	1.0550 + 0.8924i
	x61	1.2749 + 0.8538i	0.3380 + 0.5050i	0.8612 + 1.2800i
	x62	1.1556 + 1.1847i	0.4571 + 0.3499i	1.2696 + 0.8969i
	x63	1.4771 + 0.6742i	0.3216 + 0.3599i	1.0342 + 1.1181i

TABLE 77
CR 6/15	CR 8/15	CR 10/15	CR 12/15
Label (Int.)	Constellation	Label (Int.)	Constellation	Label (Int.)	Constellation	Label (Int.)	Constellation
0	0.6800 + 1.6926i	0	1.0804 + 1.3788i	0	1.6097 + 0.1548i	0	1.1980 + 1.1541i
1	0.3911 + 1.3645i	1	1.0487 + 0.9862i	1	1.5549 + 0.4605i	1	0.9192 + 1.2082i
2	0.2191 + 1.7524i	2	1.6464 + 0.7428i	2	1.3226 + 0.1290i	2	1.2778 + 0.8523i
3	0.2274 + 1.4208i	3	1.3245 + 0.9414i	3	1.2772 + 0.3829i	3	1.0390 + 0.9253i
4	0.8578 + 1.2481i	4	0.7198 + 1.2427i	4	1.2753 + 1.0242i	4	0.6057 + 1.2200i
5	0.7275 + 1.1667i	5	0.8106 + 1.0040i	5	1.4434 + 0.7540i	5	0.7371 + 1.4217i
6	0.8747 + 1.0470i	6	0.5595 + 1.0317i	6	1.0491 + 0.8476i	6	0.6678 + 1.0021i
7	0.7930 + 1.0406i	7	0.6118 + 0.9722i	7	1.1861 + 0.6253i	7	0.8412 + 0.9448i
8	0.2098 + 0.9768i	8	1.6768 + 0.2002i	8	0.9326 + 0.0970i	8	1.2128 + 0.5373i
9	0.2241 + 1.0454i	9	0.9997 + 0.6844i	9	0.8962 + 0.2804i	9	1.0048 + 0.5165i
10	0.1858 + 0.9878i	10	1.4212 + 0.4769i	10	1.1044 + 0.1102i	10	1.4321 + 0.6343i
11	0.1901 + 1.0659i	11	1.1479 + 0.6312i	11	1.0648 + 0.3267i	11	1.0245 + 0.7152i
12	0.5547 + 0.8312i	12	0.6079 + 0.6566i	12	0.7325 + 0.6071i	12	0.6384 + 0.6073i
13	0.5479 + 0.8651i	13	0.7284 + 0.6957i	13	0.8260 + 0.4559i	13	0.8175 + 0.5684i
14	0.6073 + 0.8182i	14	0.5724 + 0.7031i	14	0.8744 + 0.7153i	14	0.6568 + 0.7801i
15	0.5965 + 0.8420i	15	0.6302 + 0.7259i	15	0.9882 + 0.5300i	15	0.8311 + 0.7459i
16	1.4070 + 0.1790i	16	0.1457 + 1.4010i	16	0.1646 + 1.6407i	16	0.1349 + 1.4742i
17	1.7227 + 0.2900i	17	0.1866 + 1.7346i	17	0.4867 + 1.5743i	17	0.1105 + 1.2309i
18	1.3246 + 0.2562i	18	0.1174 + 1.1035i	18	0.1363 + 1.3579i	18	0.0634 + 0.9796i
19	1.3636 + 0.3654i	19	0.1095 + 1.0132i	19	0.4023 + 1.3026i	19	0.1891 + 1.0198i
20	1.3708 + 1.2834i	20	0.4357 + 1.3636i	20	1.0542 + 1.2584i	20	0.4142 + 1.4461i
21	1.6701 + 0.8403i	21	0.5853 + 1.6820i	21	0.7875 + 1.4450i	21	0.3323 + 1.2279i
22	1.1614 + 0.7909i	22	0.3439 + 1.0689i	22	0.8687 + 1.0407i	22	0.4998 + 0.9827i
23	1.2241 + 0.7367i	23	0.3234 + 0.9962i	23	0.6502 + 1.1951i	23	0.3467 + 1.0202i
24	0.9769 + 0.1863i	24	0.1092 + 0.6174i	24	0.0882 + 0.9745i	24	0.0680 + 0.6501i
25	0.9452 + 0.2057i	25	0.1074 + 0.6387i	25	0.2842 + 0.9344i	25	0.2016 + 0.6464i
26	1.0100 + 0.2182i	26	0.1109 + 0.6996i	26	0.1142 + 1.1448i	26	0.0719 + 0.8075i
27	0.9795 + 0.2417i	27	0.1076 + 0.7345i	27	0.3385 + 1.0973i	27	0.2088 + 0.8146i
28	0.8241 + 0.4856i	28	0.3291 + 0.6264i	28	0.6062 + 0.7465i	28	0.4809 + 0.6296i
29	0.8232 + 0.4837i	29	0.3126 + 0.6373i	29	0.4607 + 0.8538i	29	0.3374 + 0.6412i
30	0.8799 + 0.5391i	30	0.3392 + 0.6999i	30	0.7263 + 0.8764i	30	0.4955 + 0.8003i
31	0.8796 + 0.5356i	31	0.3202 + 0.7282i	31	0.5450 + 1.0067i	31	0.3431 + 0.8141i
32	0.1376 + 0.3342i	32	0.9652 + 0.1066i	32	0.2655 + 0.0746i	32	1.2731 + 0.1108i
33	0.1383 + 0.3292i	33	0.9075 + 0.1666i	33	0.2661 + 0.0759i	33	1.0794 + 0.0977i
34	0.1363 + 0.3322i	34	0.9724 + 0.1171i	34	0.4571 + 0.0852i	34	1.5126 + 0.1256i
35	0.1370 + 0.3273i	35	0.9186 + 0.1752i	35	0.4516 + 0.1062i	35	0.9029 + 0.0853i
36	0.1655 + 0.3265i	36	0.6342 + 0.1372i	36	0.2559 + 0.1790i	36	0.5429 + 0.0694i
37	0.1656 + 0.3227i	37	0.6550 + 0.1495i	37	0.2586 + 0.1772i	37	0.6795 + 0.0659i
38	0.1634 + 0.3246i	38	0.6290 + 0.1393i	38	0.3592 + 0.2811i	38	0.5628 + 0.1945i
39	0.1636 + 0.3208i	39	0.6494 + 0.1504i	39	0.3728 + 0.2654i	39	0.7326 + 0.1410i
40	0.1779 + 0.6841i	40	1.3127 + 0.1240i	40	0.7706 + 0.0922i	40	1.2283 + 0.3217i
41	0.1828 + 0.6845i	41	0.9572 + 0.4344i	41	0.7407 + 0.2260i	41	1.0269 + 0.3261i
42	0.1745 + 0.6828i	42	1.2403 + 0.2631i	42	0.6180 + 0.0927i	42	1.4663 + 0.3716i
43	0.1793 + 0.6829i	43	1.0254 + 0.4130i	43	0.6019 + 0.1658i	43	0.9085 + 0.2470i
44	0.3547 + 0.6009i	44	0.6096 + 0.4214i	44	0.6007 + 0.4980i	44	0.6160 + 0.4549i
45	0.3593 + 0.6011i	45	0.6773 + 0.4284i	45	0.6673 + 0.3928i	45	0.7818 + 0.4247i
46	0.3576 + 0.5990i	46	0.5995 + 0.4102i	46	0.4786 + 0.3935i	46	0.5938 + 0.3170i
47	0.3624 + 0.5994i	47	0.6531 + 0.4101i	47	0.5176 + 0.3391i	47	0.7600 + 0.2850i
48	0.2697 + 0.1443i	48	0.1250 + 0.1153i	48	0.0757 + 0.1003i	48	0.0595 + 0.0707i
49	0.2704 + 0.1433i	49	0.1252 + 0.1158i	49	0.0753 + 0.1004i	49	0.1722 + 0.0705i
50	0.2644 + 0.1442i	50	0.1245 + 0.1152i	50	0.0777 + 0.4788i	50	0.0599 + 0.2119i
51	0.2650 + 0.1432i	51	0.1247 + 0.1156i	51	0.0867 + 0.4754i	51	0.1748 + 0.2114i
52	0.2763 + 0.1638i	52	0.3768 + 0.1244i	52	0.1023 + 0.2243i	52	0.4134 + 0.0701i
53	0.2768 + 0.1626i	53	0.3707 + 0.1237i	53	0.1010 + 0.2242i	53	0.2935 + 0.0705i
54	0.2715 + 0.1630i	54	0.3779 + 0.1260i	54	0.1950 + 0.3919i	54	0.4231 + 0.2066i
55	0.2719 + 0.1618i	55	0.3717 + 0.1252i	55	0.1881 + 0.3969i	55	0.2979 + 0.2100i
56	0.6488 + 0.1696i	56	0.1161 + 0.3693i	56	0.0930 + 0.8122i	56	0.0638 + 0.5002i
57	0.6462 + 0.1706i	57	0.1157 + 0.3645i	57	0.2215 + 0.7840i	57	0.1905 + 0.4966i
58	0.6456 + 0.1745i	58	0.1176 + 0.3469i	58	0.0937 + 0.6514i	58	0.0617 + 0.3552i
59	0.6431 + 0.1753i	59	0.1171 + 0.3424i	59	0.1540 + 0.6366i	59	0.1810 + 0.3533i
60	0.5854 + 0.3186i	60	0.3530 + 0.3899i	60	0.4810 + 0.6306i	60	0.4630 + 0.4764i
61	0.5862 + 0.3167i	61	0.3422 + 0.3808i	61	0.3856 + 0.7037i	61	0.3231 + 0.4895i
62	0.5864 + 0.3275i	62	0.3614 + 0.3755i	62	0.3527 + 0.5230i	62	0.4416 + 0.3397i
63	0.5873 + 0.3254i	63	0.3509 + 0.3656i	63	0.3100 + 0.5559i	63	0.3083 + 0.3490i

Table 72 indicates non-uniform 16-QAM, Tables 73 to 75 indicate non-uniform 64-QAM, and tables 76 and 77 indicate non-uniform 256-QAM, and different mapping methods may be applied according to a code rate.

On the other hand, when the non-uniform constellation is designed to have the x-axis and the y-axis symmetric to each other, constellation points may be expressed similarly to those of uniform QAM and an example is illustrated as in Tables 78 to 81 presented below:

TABLE 78
y0,q	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
y2,q	0	0	0	0	0	0	0	0	1	1	1	1	1	1	1	1
y4,q	0	0	0	0	1	1	1	1	1	1	1	1	0	0	0	0
y6,q	0	0	1	1	1	1	0	0	0	0	1	1	1	1	0	0
y8,q	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1	0
Re(zq)	−x15	−x14	−x13	−x12	−x11	−x10	−x9	−x8	−x7	−x6	−x5	−x4	−x3	−x2	−x1	−1
y0,q	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
y2,q	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0
y4,q	0	0	0	0	1	1	1	1	1	1	1	1	0	0	0	0
y6,q	0	0	1	1	1	1	0	0	0	0	1	1	1	1	0	0
y8,q	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1	0
Re(zq)	1	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	x11	x12	x13	x14	x15

TABLE 79
y1,q	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
y3,q	0	0	0	0	0	0	0	0	1	1	1	1	1	1	1	1
y5,q	0	0	0	0	1	1	1	1	1	1	1	1	0	0	0	0
y7,q	0	0	1	1	1	1	0	0	0	0	1	1	1	1	0	0
y9,q	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1	0
Im(zq)	−x15	−x14	−x13	−x12	−x11	−x10	−x9	−x8	−x7	−x6	−x5	−x4	−x3	−x2	−x1	−1
y1,q	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
y3,q	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0
y5,q	0	0	0	0	1	1	1	1	1	1	1	1	0	0	0	0
y7,q	0	0	1	1	1	1	0	0	0	0	1	1	1	1	0	0
y9,q	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1	0
Im(zq)	1	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	x11	x12	x13	x14	x15

TABLE 80
X/Shape	R6/15	R7/15	R8/15	R9/15	R10/15	R11/15	R12/15	R13/15
x1	1.0003	1	1.0005	1	1.0772	1.16666667	2.5983	2.85714286
x2	1.0149	1.04	2.0897	2.78571429	2.8011	1.08333333	8.5193	4.85714286
x3	1.0158	1.04	2.0888	2.78571429	2.9634	3.33333333	6.1649	6.85714286
x4	2.6848	3	3.9345	4.85714266	4.8127	5.16666667	8.2107	8.85714286
x5	2.6903	3.04	3.9931	4.85714286	5.1864	5.75	9.9598	11
x6	2.882	3.28	5.3843	6.85714286	6.7838	7.41666667	12.0321	13.2857143
x7	2.8747	3.32	5.3893	6.85714286	7.5029	8.5	13.9574	15.7142857
x8	4.7815	5.24	7.5206	9.14285714	9.238	10.0833333	16.2598	18.1428571
x9	4.7619	5.32	7.6013	9.28571429	10.32	11.5833333	18.4269	20.7142857
x10	5.5729	6.04	9.3371	11.5714286	12.0115	13.3333333	20.9273	23.4285714
x11	5.6334	6.28	9.8429	12.2142857	13.5356	15.25	23.4863	26.2857143
x12	7.3855	8.28	11.9255	14.6428571	15.6099	17.3333333	26.4823	29.2857143
x13	7.8797	8.88	13.3561	16.4285714	17.7524	19.75	29.7085	32.4285714
x14	9.635	11.04	15.8981	19.4285714	20.5256	22.4166667	33.6247	35.7142857
x15	11.7874	13.68	19.1591	23.2857143	24.1254	25.5833333	38.5854	39.4285714

TABLE 81
	X/Shape	9/15	11/15	13/15
	x0	1	1.275373	2.568204
	x1	2.753661	3.224572	4.986168
	x2	2.754654	3.680802	6.996148
	x3	4.810415	5.509975	9.073992
	x4	4.814368	6.346779	11.17465
	x5	6.797569	8.066609	13.35998
	x6	6.812391	9.353538	15.60906
	x7	9.044328	11.04938	17.97794
	x8	9.195366	12.69977	20.46238
	x9	11.42332	14.55533	23.10439
	x10	12.08725	16.56972	25.93383
	x11	14.46334	18.82536	28.98772
	x12	16.26146	21.364	32.30898
	x13	19.19229	24.26295	35.0013
	x14	22.97401	27.70588	40.26307

Tables 78 and 79 are tables for determining the real number component Re(z_q) and the imaginary number component Im(z_q) when modulation is performed in the non-uniform 1024-QAM method. That is, Table 78 indicates the real number part of the 1024-QAM, and Table 79 indicates the imaginary number part of the 1024-QAM. In addition, Tables 80 and 81 illustrate an example of a case in which modulation is performed in the non-uniform 1024-QAM method, and show x_i values of Tables 78 and 79.

Since the non-uniform constellation method does not symmetrically map the modulation symbol onto the constellation point as shown in Tables 72 to 77, modulation symbols mapped onto constellation points may have different decoding performance. That is, bits constituting a modulation symbol may have different performance.

For example, referring to FIG. 15 illustrating an example of a case in which modulation is performed in the non-uniform 64-QAM method, a modulation symbol 10 may be configured as (y₀, y₁, y₂, y₃, y₄, y₅)=(0, 0, 1, 0, 1, 0), and performance (e.g., capacity) of bits constituting the modulation symbol 10 may have a relationship of C(y₀)>C(y₁)>C(y₂)>C(y₃)>C(y₄)>C(y₅).

In addition, it is obvious that the constellation in the uniform constellation method and the non-uniform constellation method may be rotated and/or scaled (herein, the same or different scaling factor may be applied to a real number axis and an imaginary number axis), and other variations can be applied. In addition, the illustrated constellation indicates relevant locations of the constellation points and another constellation can be derived by rotation, scaling and/or other appropriate conversion.

As described above, the modulator 130 may map modulation symbols onto constellation points by using uniform constellation methods and non-uniform constellation methods. In this case, bits constituting a modulation symbol may have different performance as described above.

LDPC codeword bits may have different codeword characteristics according to a configuration of a parity check matrix. That is, the LDPC codeword bits may have different codeword characteristics according to the number of 1 existing in the columns of the parity check matrix, that is, a column degree.

Accordingly, the interleaver 120 may interleave to map the LDPC codeword bits onto modulation symbols by considering both the codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting a modulation symbol.

In particular, since bits constituting a modulation symbol have different performance when a non-uniform QAM is used, the block interleaver 124 configures the number of columns to be identical to the number of bits constituting a modulation symbol such that one of a plurality of groups of an LDPC codeword can be mapped onto bits each of which exists on a same location of each modulation symbol.

That is, when LDPC codeword bits of high decoding performance are mapped onto high reliability bits from among bits of each modulation symbol, a receiver side may show high decoding performance, but there is a problem that the LDPC codeword bits of the high decoding performance are not received. In addition, when the LDPC codeword bits of high decoding performance are mapped onto low reliability bits from among the bits of the modulation symbol, initial reception performance is excellent, and thus, overall performance is also excellent. However, when many bits showing poor decoding performance are received, error propagation may occur.

Accordingly, when LDPC codeword bits are mapped onto modulation symbols, an LDPC codeword bit having a specific codeword characteristic is mapped onto a specific bit of a modulation symbol by considering both codeword characteristics of the LDPC codeword bits and reliability of the bits of the modulation symbol, and is transmitted to a receiver side. Accordingly, the receiver side can achieve both the high reception performance and the high decoding performance.

In this case, since the LDPC codeword is divided into groups each formed of M (=360) number of bits having the same codeword characteristic and the bits are mapped respectively onto a bit of a specific location of each modulation symbol in group units, bits having a specific codeword characteristic can be mapped onto the specific location of each modulation symbol more effectively. In addition, as described above, the number of bits forming a group may be a divisor of M. However, in this specification, the number of codeword bits forming a group will be limited to M for convenience of explanation.

That is, the modulator 130 can map bits included in a predetermined group from among the plurality of groups constituting the LDPC codeword onto a predetermined bit of each modulation symbol. Herein, each of the plurality of groups may be formed of M(=360) bits.

For example, in the case of 16-QAM, bits included in a predetermined group from among the plurality of groups may be mapped onto a first bit of each modulation symbol, or may be mapped onto a first bit and a second bit.

The modulator 130 can map bits included in a predetermined group from among the plurality of groups onto a predetermined bit of each modulation symbol for the following reasons.

As described above, the block interleaver 124 interleaves a plurality of groups of an LDPC codeword in group units, the demultiplexer demultiplexes bits output from the block interleaver 124, and the modulator 130 maps demultiplexed bits (that is, cells) onto modulation symbols serially.

Accordingly, the group interleaver 122, which is placed before the block interleaver 124, interleaves the LDPC codeword in group units such that groups including bits to be mapped onto bits of specific locations of a modulation symbol can be written in the same column of the block interleaver 124, considering a demultiplexing operation of the demultiplexer.

Specifically, the group interleaver 122 may rearrange the order of a plurality of groups of an LDPC codeword in group units such that groups including bits to be mapped onto the same location of different modulation symbols are serially arranged adjacent to one another, thereby allowing the block interleaver 122 to write a predetermined group on a predetermined column. That is, the group interleaver 122 interleaves the plurality of groups of the LDPC codeword in group units based on the above-described Tables 27 to 56, so that groups including bits to be mapped onto the same location of each modulation symbol are arranged to be adjacent to one another, and the block interleaver 124 interleaves by writing the adjacent groups on the same column.

Accordingly, the modulator 130 may generate a modulation symbol by mapping a bit output from a predetermined column of the block interleaver 124 onto a predetermined bit of the modulation symbol. In this case, bits included in one group may be mapped onto one bit of each modulation symbol or may be mapped onto two bits of each modulation symbol.

To explain detail, a case in which an LDPC codeword having a length of 16200 is modulated in the non-uniform 64-QAM method will be explained.

The group interleaver 122 divides the LDPC codeword into 16200/360(=45) groups, and interleaves the plurality of groups in group units.

In this case, the group interleaver 122 determines the number of groups to be written in each column of the block interleaver 124 based on the number of columns of the block interleaver 124, and interleaves the plurality of groups in group units based on the determined number of groups.

Herein, groups written in a same column of the block interleaver 124 may be mapped onto a single specific bit or two specific bits from among bits constituting each modulation symbol according to the number of columns of the block interleaver 124. Thus, the group interleaver 122 interleaves the plurality of groups in group units such that groups including bits required to be mapped onto a predetermined bit of each modulation symbol are adjacent to one another and serially arranged, considering bit characteristic of the modulation symbol. In this case, the group interleaver 122 may use the above-described Tables 27 to 56.

Accordingly, the groups which are adjacent to one another in the LDPC codeword interleaved in group units may be written in the same column of the block interleaver 124, and the bits written in the same column may be mapped onto a single specific bit or two specific bits of each modulation symbol by the modulator 130.

For example, it is assumed that the block interleaver 124 includes as many columns as the number of bits constituting a modulation symbol, that is, six (6) columns. In this case, each column of the block interleaver 124 may be divided into a first part including 2520 rows and a second part including 180 rows, as shown in Table 58 or 61.

Accordingly, the group interleaver 122 performs group interleaving such that 2520/360(=7) groups to be written in the first part of each column of the block interleaver 124 from among the plurality of groups are serially arranged to be adjacent to one another. Accordingly, the block interleaver 124 writes the seven (7) groups on the first part of each column and divides the bits included in the other three (3) groups and writes these bits on the second part of each column.

Thereafter, the block interleaver 124 reads the bits written in each row of the first part of the plurality of columns in the row direction, and reads the bits written in each row of the second part of the plurality of columns in the row direction.

That is, the block interleaver 124 may output the bits written in each row of the plurality of columns, from the bit written in the first row of the first column to the bit written in the first row of the sixth column, sequentially like (q₀, q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, q₁₀, q₁₁, . . . )

In this case, when the demultiplexer is not used or the demultiplexer outputs serially bits input to the demultiplexer without changing the order of the bits, the LDPC codeword bits output from the block interleaver 124, (q₀, q₁, q₂, q₃, q₄, q₅), (q₆, q₇, q₈, q₉, q₁₀, q₁₁), . . . , etc. are modulated by the modulator 130. That is, the LDPC codeword bits output from the block interleaver 124, (q₀, q₁, q₂, q₃, q₄, q₅), (q₆, q₇, q₈, q₉, q₁₀, q₁₁), . . . , etc. configure cells (y_0,0, y_1,0, . . . , y_5,0), (y_0,1, y_1,1, . . . , y_5,1), . . . , etc. and the modulator 130 generates a modulation symbol by mapping the cells onto constellation points.

Accordingly, the modulator 130 may map bits output from a same column of the block interleaver 124 onto a single specific bit of bits constituting each modulation symbol. For example, the modulator 130 may map bits included in a group written in the first column of the block interleaver 124, that is, (q₀, q₆, . . . ), onto the first bit of each modulation symbol, and also, all bits written in the first column may be bits which are determined to be mapped onto the first bit of each modulation symbol according to a codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol.

As described above, the group interleaver 122 may interleave a plurality of groups of an LDPC codeword in group units such that the groups including bits to be mapped onto a single bit of a specific location of each modulation symbol are written in a specific column of the block interleaver 124.

On the other hand, it is assumed that the block interleaver 124 includes as many columns as half of the number of bits constituting a modulation symbol, that is, three (3) columns. In this case, each column of the block interleaver 124 is not divided into parts as shown in Table 60 and 5400 bits are written in each column.

Accordingly, the group interleaver 122 performs group interleaving such that 5400/360(=15) groups to be written in each column of the block interleaver 124 from among the plurality of groups are serially arranged to be adjacent to one another. Accordingly, the block interleaver 124 writes the 15 groups on each column.

Thereafter, the block interleaver 124 may read bits written in each row of the plurality of columns in the row direction.

That is, the block interleaver 124 may output the bits written in each row of the plurality of columns, from the bit written in the first row of the first column to the bit written in the first row of the third column, sequentially like (q₀, q₁, q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, q₁₀, q₁₁, . . . )

In this case, the demultiplexer demultiplexes the LDPC codeword bits output from the block interleaver 124 based on Table 63 described above, and output cells likes (y_0,0, y_1,0, . . . , y_5,0)=(q₀, q₂, q₄, q₁, q₃, q₅), (y_0,1, y_1,1, . . . , y_5,1)=(q₆, q₈, q₁₀, q₇, q₉, q₁₁) . . . , etc. and the modulator 130 generates a modulation symbol by mapping the cells onto constellation points.

Accordingly, the modulator 130 may map bits output from the same column of the block interleaver 124 onto two specific bits of each modulation symbol. For example, the modulator 130 may map (q₀, q₆, . . . ) from among the bits (q₀, q₃, q₆, q₉, . . . ) included in the group written in the first column in the block interleaver 124 onto the first bit of each modulation symbol, and may map (q₃, q₉, . . . ) on the fifth bit of each modulation symbol. The bits written in the first column are bits which are determined to be mapped onto the first bit and the fifth bit of each modulation symbol according to the codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol. Herein, the first bit of the modulation symbol is a bit for determining a sign of the real number component Re(z_q) of a constellation point onto which the modulation symbol is mapped, and the fifth bit of the modulation symbol is a bit for determining a relatively small size of the constellation point onto which the modulation symbol is mapped.

As described above, the group interleaver 122 may interleave the plurality of groups of the LDPC codeword in group units such that groups including bits to be mapped onto two bits of specific locations of a modulation symbol are written in a specific column of the block interleaver 124.

Hereinafter, exemplary embodiments will be explained in detail.

First, according to a first exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 10/15, 11/15, 12/15 and 13/15 and generates an LDPC codeword formed of 16200 bits (N_ldpc=16200), and the modulator 130 uses the non-uniform 16-QAM modulation method corresponding to the code rate based on Table 72.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 82 presented below:

TABLE 82
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	7	17	33	31	26	10	32	41	28	8	24	42	20	9	35	43	22	12	38	3	5	14	37
12/15, 13/15	40	19	16	27	39	25	4	21	1	23	18	36	0	6	11	34	2	29	15	30	13	44

Table 82 defines π(j) in Equation 11 and is identical to Table 27 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 83 presented below:

TABLE 83
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	35	31	39	19	29	20	36	0	9	13	5	37	17	43	21	41	25	1	33	24	12	30	16
12/15, 13/15	32	10	28	4	26	8	40	42	3	6	2	38	14	34	22	18	27	23	7	11	25	44

Table 83 defines π(j) in Equation 12 and is identical to Table 42 described above.

Herein, a result of group interleaving based on Equation 11 and Table 82 and a result of group interleaving based on Equation 12 and Table 83 are identical to each other. This is because Equation 11 and Equation 12 have an inverse relationship to each other, and Table 82 and Table 83 have an inverse relationship to each other. This is applied to exemplary embodiments presented below.

In these cases, the block interleaver 124 in which the number of columns is four (4), the number of rows of the first part is 3960(=360×11), and the number of rows of the second part is 180 according to Table 57 or 61 may be used.

Accordingly, 11 groups (X₇, X₁₇, X₃₃, X₃₁, X₂₆, X₁₀, X₃₂, X₄₁, X₂₈, X₈, X₂₄) constituting an LDPC codeword are input to the first part of the first column of the block interleaver 124, 11 groups (X₄₂, X₂₀, X₉, X₃₅, X₄₃, X₂₂, X₁₂, X₃₈, X₃, X₅, X₁₄) are input to the first part of the second column of the block interleaver 124, 11 groups (X₃₇, X₄₀, X₁₉, X₁₆, X₂₇, X₃₉, X₂₅, X₄, X₂₁, X₁, X₂₃) are input to the first part of the third column of the block interleaver 124, and 11 groups (X₁₈, X₃₆, X₀, X₆, X₁₁, X₃₄, X₂, X₂₉, X₁₅, X₃₀, X₁₃) are input to the first part of the fourth column of the block interleaver 124.

In addition, a group X₄₄ is input to the second part of the block interleaver 124. Specifically, bits constituting the group X₄₄ are input to the rows of the first column of the second part serially, input to the rows of the second column serially, input to the rows of the third column serially, and finally input to the rows of the fourth column serially.

In addition, the block interleaver 124 may output the bits input to the first row to the last row of each column serially, and the bits output from the block interleaver 124 may be input to the modulator 130 serially. In this case, the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

Accordingly, one bit included in each of groups X₇, X₄₂, X₃₇ and X₁₈ constitute a single modulation symbol.

According to an exemplary embodiment, one bit included in each of the groups X₇, X₄₂, X₃₇ and X₁₈ constitute a single modulation symbol based on group interleaving and block interleaving. In addition to the above-described method, other methods for constituting a single modulation symbol with one bit included in each of the groups X₇, X₄₂, X₃₇ and X₁₈ may be included in the inventive concept.

The performance achieved when a method according to a first exemplary embodiment is used is illustrated in FIG. 20. Referring to FIG. 20, when the non-uniform 16-QAM modulation method is used, high bit error rate and frame error rate (BER/FER) performance can be shown in a specific SNR region.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterleaver and a decoder to be explained later in reference to FIG. 27, respectively.

According to a second exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 16200 bits (N_ldpc=16200), and the modulator 130 uses the non-uniform 64-QAM modulation method corresponding to a code rate based on Tables 73 or 75.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 84 presented below:

TABLE 84
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	32	4	23	27	35	24	16	39	5	22	33	40	18	13	8	6	37	34	0	15	21	38	30
8/15, 9/15	26	14	17	10	31	25	28	12	1	29	9	41	3	20	19	36	11	7	2	42	43	44

Table 84 defines π(j) in Equation 11 and is identical to Table 29 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 85 presented below:

TABLE 85
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	18	31	41	35	1	8	15	40	14	33	26	39	30	13	24	19	6	25	12	37	36	20	9
8/15, 9/15	2	5	28	23	3	29	32	22	27	0	10	17	4	38	16	21	7	11	34	42	43	44

Table 85 defines π(j) in Equation 12 and is identical to Table 44 described above.

In these cases, the block interleaver 124 in which the number of columns is six (6), the number of rows of the first part is 2520(=360×7), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterleaver and a decoder to be explained later in reference to FIG. 27, respectively.

The performance achieved when a method according to the second exemplary embodiment is used is illustrated in FIG. 21. Referring to FIG. 21, when the non-uniform 64-QAM modulation method is used, high BER/FER performance can be shown in a specific SNR region.

According to a third exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 10/15, 11/15, 12/15, and 13/15 and generates an LDPC codeword formed of 16200 bits (N_ldpc=16200), and the modulator 130 uses the non-uniform 256-QAM modulation method corresponding to the code rate based on Tables 76 and 77.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 86 presented below:

TABLE 86
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	28	6	15	8	0	22	37	35	21	26	7	12	27	1	32	33	13	11	10	18	34	9	39
12/15, 13/15	38	24	17	29	25	5	16	30	2	4	19	23	14	20	3	31	36	40	41	42	43	44

Table 86 defines π(j) in Equation 11 and is identical to Table 31 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 87 presented below:

TABLE 87
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	4	13	31	37	32	28	1	10	3	21	18	17	11	16	35	2	29	25	19	33	36	8	5
12/15, 13/15	34	24	27	9	12	0	26	30	38	14	15	20	7	39	6	23	22	40	41	42	43	44

Table 87 defines π(j) in Equation 12 and is identical to Table 46 described above.

In these cases, the block interleaver 124 in which the number of columns is eight (8), the number of rows of the first part is 1800(=360×5), and the number of rows of the second part is 225 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterleaver and a decoder to be explained later in reference to FIG. 27, respectively.

According to a fourth exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 16200 bits (N_ldpc=16200), and the modulator 130 uses the non-uniform 1024-QAM modulation method corresponding to the code rate based on Tables 78 to 81.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 88 presented below:

TABLE 88
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	16	13	1	25	24	33	4	29	32	30	0	17	22	18	8	9	27	11	37	35	12	15	10
8/15, 9/15	20	5	6	36	38	2	26	14	7	19	3	21	23	31	34	28	39	40	41	42	43	44

Table 88 defines π(j) in Equation 11 and is identical to Table 33 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 89 presented below:

TABLE 89
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	10	2	28	33	6	24	25	31	14	15	22	17	20	1	30	21	0	11	13	32	23	34	12
8/15, 9/15	35	4	3	29	16	38	7	9	36	8	5	37	19	26	18	27	39	40	41	42	43	44

Table 89 defines π(j) in Equation 12 and is identical to Table 48 described above.

In these cases, the block interleaver 124 in which the number of columns is 10, the number of rows of the first part is 1440(=360×4), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterleaver and a decoder to be explained later in reference to FIG. 27, respectively.

The performance achieved when a method according to the fourth exemplary embodiment is used is illustrated in FIG. 22. Referring to FIG. 22, when the non-uniform 1024-QAM modulation method according to an exemplary embodiment is used, high BER/FER performance can be shown in a specific SNR region.

According to a fifth exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 64800 bits (N_ldpc=64800), and the modulator 130 uses the non-uniform 256-QAM modulation method corresponding to the code rate based on Tables 76 and 77.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 90 presented below:

TABLE 90
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	48	4	15	97	108	76	1	174	61	0	59	71
7/15,	138	35	62	43	86	153	73	173	165	23	49	91
8/15,	110	20	58	42	40	403	159	83	127	111	63	89
9/15	123	29	141	51	21	17	45	126	150	3	168	41
	14	131	82	134	55	33	50	84	23	105	6	145
	30	151	18	145	129	53	100	22	107	16	170	143
	37	24	130	136	161	75	29	9	47	60	162	146
	13	85	88	135	116	12	163	20	46	87	94	139
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	120	175	167	114	65	93	101	19	112	100	152
	7/15,	5	169	59	77	149	26	36	25	56	156	155
	8/15,	11	52	144	142	113	154	44	96	93	66	122
	9/15	106	124	64	147	78	8	118	113	39	59	140
		7	27	132	92	115	164	74	10	68	102	67
		121	38	57	95	90	172	81	158	171	32	119
		137	157	70	164	31	34	166	128	117	125	2
		54	72	160	176	177	178	179

Table 90 defines π(j) in Equation 11 and is identical to Table 35 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 91 presented below:

TABLE 91
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	9	6	160	78	1	35	102	103	26	145	111	58
7/15,	32	139	42	40	105	100	144	115	154	136	97	155
8/15,	169	146	0	33	98	72	59	120	173	96	41	129
9/15	90	152	11	174	29	110	143	5	38	85	70	47
	107	65	171	130	65	3	17	37	121	18	111	51
	103	165	158	87	137	12	127	68	69	82	159	76
	23	172	91	71	61	126	60	103	149	64	118	39
	142	148	167	100	31	156	14	79	36	125	135	132
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	166	161	92	2	124	74	117	19	163	73	122
	7/15,	24	41	138	128	69	50	80	49	26	64	75
	8/15,	43	10	147	8	25	56	83	16	67	114	112
	9/15	133	94	53	99	162	27	170	163	57	131	34
		153	101	81	123	4	21	46	55	20	88	15
		51	157	119	140	93	106	62	95	164	141	150
		77	116	22	28	63	45	44	151	234	52	275
		30	7	13	179	178	177	176

Table 91 defines π(j) in Equation 12 and is identical to Table 50 described above.

In these cases, the block interleaver 124 in which the number of columns is 8, the number of rows of the first part is 7920(=360×22), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer (not shown) may be omitted or the demultiplexer (not shown) may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterleaver and a decoder to be explained later in reference to FIG. 27, respectively.

In the first to fifth exemplary embodiments, when the grouping interleaving is performed by using Equation 11, a value of π(j) is applied as an index of an input group, and, when the group interleaving is performed by using Equation 12, a value of π(j) is applied as an index of an output group. Therefore, Equation 11 and 12 have an inverse relationship

In addition, the above-described first to fifth exemplary embodiments are merely an example for explaining the above inverse relationship and various tables described in this description may have the same inverse relationship like the first to fifth exemplary embodiments.

The transmitter apparatus 100 may modulate a signal mapped onto a constellation and may transmit the signal to the receiver apparatus (for example, a receiver apparatus 2700 of FIG. 27). For example, the transmitter apparatus 200 may map a signal mapped onto a constellation onto an Orthogonal Frequency Division Multiplexing (OFDM) frame by using the OFDM method, and may transmit the signal to the receiver apparatus 2700 via an allocated channel.

Exemplary Embodiment 2

Use of Block-Row Interleaver

According to another exemplary embodiment, the interleaver 120 may interleave an LDPC codeword in other methods, different from the methods described in the exemplary embodiment 1 beginning at paragraph [0127] above, and may map bits included in a predetermined group from among a plurality of groups constituting the interleaved LDPC codeword onto a predetermined bit of a modulation symbol. This will be explained in detail with reference to FIG. 23.

Referring to FIG. 23, the interleaver 120 includes a parity interleaver 121, a group interleaver (or a group-wise interleaver 122), a group twist interleaver 123 and a block-row interleaver 125. Herein, the parity interleaver 121 and the group twist interleaver 123 perform the same functions as in the exemplary embodiment 1 described above. and thus, a detailed description of these elements is omitted.

The group interleaver 122 may divide a parity-interleaved LDPC codeword into a plurality of groups, and may rearrange the order of the plurality of groups.

In this case, the operation of dividing the parity-interleaved LDPC codeword into the plurality of groups is the same as in the exemplary embodiment 1, and thus, a detailed description thereof is omitted.

The group interleaver 122 interleaves an LDPC codeword in group units. That is, the group interleaver 122 may rearrange the order of the plurality of groups in the LDPC codeword in group units by changing locations of the plurality of groups constituting the LDPC codeword.

In this case, the group interleaver 122 may interleave the LDPC codeword in group units by using Equation 13

Y _j =X _π(j)(0≦j<N_group)  (13),

where X_j is the j^th group before group interleaving, and Y_j is the j^th group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 92 to 106 presented below.

For example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 92 or 93 presented below:

TABLE 92
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	7	42	37	18	17	20	40	36	33	9	19	0	31	35	16	6	26	43	27	11	10	22	39
12/15, 13/15	34	32	12	25	2	41	38	4	29	28	3	21	15	8	5	1	30	24	14	23	13	44

TABLE 93
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	6	25	25	4	34	7	24	0	11	14	43	20	21	30	40	31	12	13	33	5	8	32	36
12/15, 13/15	33	9	17	37	35	23	18	39	1	22	3	24	28	2	19	41	26	10	16	42	27	29

In the case of Table 92, Equation 13 may be expressed as Y₀=X_π(0)=X₇, Y₁=X_π(1)=X₄₂, Y₂=X_π(2)=X₃₇, . . . , Y₄₃=X_π(43)=X₁₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 7^th group to the 0^th group, the 42^nd group to the 1^st group, the 37^th group to the 2^nd group, . . . , the 13^th group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 93, Equation 13 may be expressed as Y₀=X_π(0)=X₆, Y₁=X_π(1)=X₁₅, Y₂=X_π(2)=X₂₅, . . . , Y₄₃=X_π(43)=X₂₇, and Y₄₄=X_π(44)=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 6^th group to the 0^th group, the 15^th group to the 1^st group, the 25^th group to the 2^nd group, . . . , the 27^th group to the 43^rd group, and the 29^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 94 or 95 presented below:

TABLE 94
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	32	39	8	38	25	3	4	5	6	30	28	20	23	22	37	26	12	19	27	33	34	14	1
8/15, 9/15	36	35	40	0	17	29	11	24	18	15	10	9	7	16	13	21	31	41	2	42	43	44

TABLE 95
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	32	4	23	27	35	24	16	39	5	22	33	40	18	13	8	6	37	34	0	15	21	18	30
8/15, 9/15	26	14	17	10	31	25	28	12	1	29	9	41	3	20	19	35	11	7	2	42	43	44

In the case of Table 94, Equation 13 may be expressed as Y₀=X_π(0)=X₃₂, Y₁=X_π(1)=X₃₉, Y₂=X_π(2)=X₈, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 32^nd group to the 0^th group, the 39^th group to the 1^st group, the 8^th group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 95, Equation 13 may be expressed as Y₀=X_π(0)=X₃₂, Y₁=X_π(1)=X₄, Y₂=X_π(2)=X₂₃, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 32^nd group to the 0^th group, the 4^th group to the 1^st group, the 23^th group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 96 or 97 presented below:

TABLE 96
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	28	22	7	33	34	17	30	14	6	37	12	13	9	29	2	20	15	35	27	11	39	25	4
12/15, 13/15	3	8	21	1	10	38	5	19	31	0	26	32	18	24	16	23	36	40	41	42	43	44

TABLE 97
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	21	9	13	17	33	38	44	42	8	1	11	16	18	32	39	3	10	32	12	6	31	5	41
12/15, 13/15	35	0	23	14	15	7	19	41	32	20	24	10	2	34	36	40	4	25	26	27	28	29

In the case of Table 96, Equation 13 may be expressed as Y₀=X_π(0)=X₂₈, Y₁=X_π(1)=X₂₂, Y₂=X_π(2)=X₇, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 28^th group to the 0^th group, the 22^nd group to the 1^st group, the 7^th group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 97, Equation 13 may be expressed as Y₀=X_π(0)=X₂₁, Y₁=X_π(1)=X₉, Y₂=X_π(2)=X₁₃, . . . , Y₄₃=X_π(43)=X₂₈, and Y₄₄=X_π(44)=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 21^st group to the 0^th group, the 9^th group to the 1^st group, the 13^th group to the 2^nd group, . . . , the 28^th group to the 43^rd group, and the 29^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 98 or 99 presented below:

TABLE 98
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	16	24	32	22	27	12	5	2	19	31	13	33	30	18	11	15	6	26	3	34	1	4	0
8/15, 9/15	8	37	10	36	14	21	28	25	29	17	9	35	20	38	7	23	39	40	41	42	43	44	—

TABLE 99
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	16	34	8	7	1	40	24	30	0	33	12	13	11	44	21	10	27	42	23	25	14	15	4
8/15, 9/15	9	18	28	41	26	35	22	19	17	6	5	31	20	32	36	29	43	2	3	37	38	39

In the case of Table 98, Equation 13 may be expressed as Y₀=X_π(0)=X₁₆, Y₁=X_π(1)=X₂₄, Y₂=X_π(2)=X₃₂, . . . , Y₄₃=X_π(43)=X₄₃, and Y₄₄=X_π(44)=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 16^th group to the 0^th group, the 24^th group to the 1^st group, the 32^nd group to the 2^nd group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 99, Equation 13 may be expressed as Y₀=X_π(0)=X₁₆, Y₁=X_π(1)=X₃₄, Y₂=X_π(2)=X₈, . . . , Y₄₃=X_π(43)=X₃₈, and Y₄₄=X_π(44)=X₃₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 16^th group to the 0^th group, the 34^th group to the 1^st group, the 8^th group to the 2^nd group, . . . , the 38^th group to the 43^rd group, and the 39^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 100 or 101 presented below:

TABLE 100
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	48	152	156	93	113	74	172	31	4	138	155	66
7/15,	166	97	62	80	123	140	102	171	128	108	43	58
8/15,	119	125	1	153	40	51	82	151	37	2	174	73
9/15	148	130	85	0	165	83	45	33	129	136	88	59
	84	100	75	116	170	91	63	3	28	22	29	12
	41	6	16	47	20	114	99	52	106	145	170	60
	142	64	27	121	146	94	101	26	133	147	132	38
	25	44	8	115	95	70	72	109	56	96	118	164
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	39	10	81	34	15	35	110	122	69	68	158
	7/15,	79	14	67	32	117	76	86	42	141	131	30
	8/15,	103	21	134	18	24	13	61	173	159	17	55
	9/15	23	127	126	50	53	161	135	71	59	111	150
		175	5	69	168	106	107	9	163	167	169	11
		46	65	77	144	321	7	143	162	87	98	149
		137	139	19	36	154	78	92	57	157	54	112
		90	104	160	176	177	178	179

TABLE 101
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	48	4	15	97	108	76	1	174	61	0	59	71
7/15,	138	35	62	43	86	153	73	178	165	23	49	91
8/15,	110	80	58	42	40	103	159	83	127	111	63	89
9/15	123	79	141	51	21	17	45	126	150	3	168	41
	14	131	82	134	55	33	50	84	28	105	6	145
	30	151	18	148	129	53	100	22	107	16	170	143
	37	24	130	136	161	75	29	9	47	60	162	148
	18	85	88	135	116	12	163	20	46	87	54	139
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	120	175	167	114	65	98	101	19	112	109	152
	7/15,	5	169	99	77	149	26	36	25	56	156	155
	8/15,	11	52	144	141	133	154	44	96	93	66	122
	9/15	106	124	54	147	78	8	118	113	39	69	140
		7	27	132	92	115	164	74	10	68	102	67
		121	38	57	95	90	172	81	158	171	32	119
		137	157	70	104	31	34	166	239	117	125	2
		54	72	100	176	177	178	179

In the case of Table 100, Equation 13 may be expressed as Y₀=X_π(0)=X₄₈, Y₁=X_π(1)=X₁₅₂, Y₂=X_π(2)=X₁₅₆, . . . , Y₁₇₈=X_π(178)=X₁₇₈, and Y₁₇₉=X_π(179)=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 48^th group to the 0^th group, the 152^nd group to the 1^st group, the 156^th group to the 2^nd group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In the case of Table 101, Equation 13 may be expressed as Y₀=X_π(0)=X₄₈, Y₁=X_π(1)=X₄, Y₂=X_π(2)=X₁₅, . . . , Y₁₇₈=X_π(178)=X₁₇₈, and Y₁₇₉=X_π(179)=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 48^th group to the 0^th group, the 4^th group to the 1^st group, the 15^th group to the 2^nd group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 102 presented below:

TABLE 102
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15	53	71	135	172	164	8	114	126	3	63	106	154
	147	46	57	178	170	5	39	109	129	68	67	119
	125	33	43	48	105	139	117	75	85	9	29	60
	76	131	116	0	59	10	12	158	136	176	161	58
	81	134	130	177	23	55	174	118	6	94	124	83
	166	88	132	173	133	32	64	19	72	123	152	91
	112	82	101	146	110	121	34	69	30	90	144	103
	62	16	142	168	2	149	111	18	65	13	162	137
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15	159	98	143	120	28	51	151	115	179	11	108
		86	157	87	175	102	15	54	50	141	163	38
		84	89	74	100	155	148	49	61	27	107	90
		70	25	73	153	20	150	80	42	45	165	79
		1	56	44	167	104	35	113	4	47	66	21
		122	7	17	145	171	99	156	95	160	36	40
		93	128	14	52	140	127	97	77	92	78	37
		41	138	169	22	24	26	31

In the case of Table 102, Equation 13 may be expressed as Y₀=X_π(0)=X₅₃, Y₁=X_π(1)=X₇₁, Y₂=X_π(2)=X₁₃₅, . . . , Y₁₇₈=X_π(178)=X₂₆, and Y₁₇₉=X_π(179)=X₃₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 53^rd group to the 0^th group, the 71^st group to the 1^st group, the 135^th group to the 2nd group, . . . , the 26^th group to the 178^th group, and the 31^st group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 103 presented below:

TABLE 103
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
8/15	71	36	38	78	140	35	175	171	104	87	110	63
	122	69	10	67	49	158	97	96	128	94	75	66
	141	157	74	85	52	31	166	27	159	103	89	17
	26	101	170	58	80	46	25	123	160	135	9	56
	148	20	116	125	173	68	51	30	112	163	106	3
	24	167	32	102	161	83	43	44	88	100	134	146
	115	95	177	151	130	0	64	91	165	73	179	136
	61	119	8	105	42	99	117	41	1	155	72	178
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	8/15	176	34	145	154	84	62	76	53	142	33	127
		28	138	172	143	107	93	12	98	23	108	111
		29	50	149	137	109	174	57	47	164	14	144
		7	90	65	169	21	153	131	59	60	120	40
		86	6	82	19	156	162	124	118	132	92	133
		81	77	13	39	29	114	22	168	126	55	70
		152	150	45	48	37	2	147	15	139	129	54
		121	113	11	4	5	16	18

In the case of Table 103, Equation 13 may be expressed as Y₀=X_π(0)=X₇₁, Y₁=X_π(1)=X₃₆, Y₂=X_π(2)=X₃₈, . . . , Y₁₇₈=X_π(178)=X₁₆, and Y₁₇₉=X_π(179)=X₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 71^st group to the 0^th group, the 36^th group to the 1^st group, the 38^th group to the 2^nd group, . . . , the 16^th group to the 178^th group, and the 18^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 104 presented below.

TABLE 104
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	111	39	34	100	48	155	173	120	65	101	115	58
	141	49	45	60	81	112	125	12	165	68	55	104
	172	170	119	93	117	2	151	162	163	164	96	41
	133	138	121	108	42	75	26	154	174	139	147	69
	40	124	143	140	51	36	50	74	11	160	159	137
	88	31	158	10	175	62	116	92	13	177	176	152
	95	14	64	149	59	9	54	23	99	77	136	134
	71	37	30	150	169	166	123	89	8	72	61	16
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	63	148	3	142	78	105	94	56	67	1	130
		84	47	24	16	167	44	98	19	0	113	161
		46	21	52	22	146	126	97	109	102	80	86
		110	91	33	6	82	17	135	114	87	76	70
		86	90	5	57	107	18	25	144	29	32	79
		157	73	4	35	27	132	168	145	127	106	20
		153	171	103	38	53	7	131	178	179	122	43
		128	129	156	28	83	85	118

In the case of Table 104, Equation 13 may be expressed as Y₀=X_π(0)=X₁₁₁, Y₁=X_π(1)=X₃₉, Y₂=X_π(2)=X₃₄, . . . , Y₁₇₈=X_π(178)=X₈₅, and Y₁₇₉=X_π(179)=X₁₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 111^th group to the 0^th group, the 39^th group to the 1^st group, the 34^th group to the 2^nd group, . . . , the 85^th group to the 178^th group, and the 118^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 105 presented below:

TABLE 105
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	89	20	72	104	85	172	13	165	64	118	109	74
	125	28	95	82	2	114	127	19	140	32	81	67
	12	175	52	96	44	105	93	14	168	176	98	36
	139	160	122	31	3	112	62	34	146	170	10	90
	61	130	150	154	70	116	55	83	164	129	124	174
	87	132	179	156	80	117	94	108	73	39	157	167
	113	115	88	9	149	22	11	75	102	6	60	138
	63	40	42	37	0	121	120	92	80	111	47	45
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	99	166	177	126	50	84	35	21	145	152	178
		23	103	169	137	153	26	7	33	86	158	159
		48	53	58	143	136	131	66	18	91	38	101
		65	49	110	77	161	5	155	59	1	78	4
		17	97	106	15	173	171	144	162	76	119	46
		133	54	100	51	79	151	148	123	16	68	107
		134	128	43	69	71	56	41	147	142	163	57
		135	141	8	24	25	27	29

In the case of Table 105, Equation 13 may be expressed as Y₀=X_π(0)=X₈₉, Y₁=X_π(1)=X₂₀, Y₂=X_π(2)=X₇₂, . . . , Y₁₇₈=X_π(178)=X₂₇, and Y₁₇₉=X_π(179)=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 89^th group to the 0^th group, the 20^th group to the 1^st group, the 72^nd group to the 2^nd group, . . . , the 27^th group to the 178^th group, and the 29^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 106 presented below:

TABLE 106
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
12/15	51	6	75	108	93	47	168	15	122	14	42	113
	11	111	21	107	97	62	31	165	176	95	71	30
	162	156	119	2	137	86	81	59	164	144	130	0
	79	157	172	57	106	87	32	76	52	160	178	65
	84	60	171	22	61	23	101	67	96	92	167	179
	80	154	110	151	163	143	17	99	127	98	27	153
	117	34	142	43	155	19	39	112	64	89	46	77
	66	135	49	131	63	166	12	116	5	138	55	72
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	12/15	136	69	147	159	91	3	129	58	68	125	161
		38	54	83	175	152	100	134	45	124	40	36
		114	33	103	40	158	148	78	140	30	74	121
		7	53	29	44	133	150	24	26	118	85	128
		126	35	141	104	123	139	145	4	105	20	120
		174	70	50	88	56	82	73	9	173	132	48
		170	10	102	13	28	94	169	109	146	177	115
		41	149	16	1	8	18	25

In the case of Table 106, Equation 13 may be expressed as Y₀=X_π(0)=X₅₁, Y₁=X_π(1)=X₆, Y₂=X_π(2)=X₇₅, . . . , Y₁₇₈=X_π(178)=X₁₈, and Y₁₇₉=X_π(179)=X₂₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 51^st group to the 0^th group, the 6^th group to the 1^st group, the 75^st group to the 2^nd group, . . . , the 18^th group to the 178^th group, and the 25^th group to the 179^th group.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups in group units by using Equation 13 and Tables 92 to 106.

On the other hand, since the order of the groups constituting the LDPC codeword is rearranged in group units by the group interleaver 122, and then, the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 19 to 106 in relation to π(j).

In addition, the group interleaver 122 may interleave the LDPC codeword in group units by using Equation 14 presented below:

Y _π(j) =X _j(0≦j<N_group)  (14),

where X_j is the jth group before group interleaving, and Y_j is the jth group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 107 to 121 presented below.

For example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 107 or 108 presented below:

TABLE 107
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	11	38	27	33	30	37	15	0	36	9	20	19	25	43	41	35	14	4	3	10	5	34	21
12/15, 13/15	42	40	26	16	18	32	31	39	12	24	8	23	13	7	2	29	22	6	28	2	17	44

TABLE 108
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	7	31	36	33	3	19	0	5	20	24	40	8	16	17	5	1	41	25	29	37	11	12	32
12/15, 13/15	28	6	2	39	43	25	44	13	15	21	23	4	27	22	26	18	33	14	33	42	10	34

In the case of Table 107, Equation 14 may be expressed as X₀=Y_π(0)=Y₁₁, X₁=Y_π(1)=Y₃₈, X₂=Y_π(2)=Y₂₇, . . . , X₄₃=Y_π(43)=Y₁₇, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 11^th group, the 1^st group to the 38^th group, the 2^nd group to the 27^th group, . . . , the 43^rd group to the 17^th group, and the 44^th group to the 44^th group.

In the case of Table 108, Equation 14 may be expressed as X₀=Y_π(0)=Y₇, X₁=Y_π(1)=Y₃₁, X₂=Y_π(2)=Y₃₆, . . . , X₄₃=Y_π(43)=Y₁₀, and X₄₄=Y_π(44)=Y₃₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 7^th group, the 1^st group to the 31^th group, the 2^nd group to the 36^th group, . . . , the 43^rd group to the 10^th group, and the 44^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 109 or 110 presented below:

TABLE 109
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	26	22	41	5	6	7	8	35	2	34	33	29	16	37	21	32	36	27	31	17	11	38	13
8/15, 9/15	12	30	4	15	18	10	28	9	39	0	19	20	24	23	14	3	1	25	40	42	43	44

TABLE 110
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	18	31	41	35	1	8	15	40	14	13	26	39	30	13	24	19	6	25	12	37	16	20	9
8/15, 9/15	2	5	28	23	3	29	32	22	27	0	10	17	4	38	16	21	7	11	34	42	43	44

In the case of Table 109, Equation 14 may be expressed as X₀=Y_π(0)=Y₂₆, X₁=Y_π(1)=Y₂₂, X₂=Y_π(2)=Y₄₁, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 26^th group, the 1^st group to the 22^nd group, the 2^nd group to the 41^th group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 110, Equation 14 may be expressed as X₀=Y_π(0)=Y₁₈, X₁=Y_π(1)=Y₃₁, X₂=Y_π(2)=Y₄₁, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 18^th group, the 1^st group to the 31^st group, the 2^nd group to the 41^st group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 111 or 112 presented below:

TABLE 111
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	32	26	14	23	22	29	8	2	24	12	27	19	10	11	7	16	37	5	35	30	15	25	1
12/15, 13/15	38	36	21	33	18	0	13	6	31	34	3	4	17	39	9	28	20	40	41	42	43	44

TABLE 112
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
10/15, 11/15,	24	9	35	15	39	21	19	28	8	1	34	10	18	2	26	27	11	3	12	29	32	0	17
12/15, 13/15	25	23	40	41	42	43	44	18	20	31	4	36	23	17	11	5	34	38	22	7	30	6

In the case of Table 111, Equation 14 may be expressed as X₀=Y_π(0)=Y₃₂, X₁=Y_π(1)=Y₂₆, X₂=Y_π(2)=Y₁₄, . . . , X₄₃=Y_π(43)=Y₄₃, X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 32^nd group, the 1^st group to the 26^th group, the 2^nd group to the 14^th group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 112, Equation 14 may be expressed as X₀=Y_π(0)=Y₂₄, X₁=Y_π(1)=Y₉, X₂=Y_π(2)=Y₃₅, . . . , X₄₃=Y_π(43)=Y₃₀, and X₄₄=Y_π(44)=Y₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 24^th group, the 1^st group to the 9^th group, the 2^nd group to the 35^th group, . . . , the 43^rd group to the 30^th group, and the 44^th group to the 6^th group.

In another example, when the length N_ldpc of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 113 or 114 presented below:

TABLE 113
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	22	20	7	18	21	6	16	37	23	33	25	14	5	10	27	15	0	32	13	8	35	28	3
8/15, 9/15	38	1	30	17	4	29	31	12	9	2	11	19	34	26	24	36	39	40	41	42	43	44

TABLE 114
	Order of bits group to be block interleaved
Code Rate	π(j) (0 ≦ j < 45)
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44
6/15, 7/15,	8	4	40	41	22	33	32	3	2	23	15	12	10	11	20	21	0	11	24	30	35	14	29
8/15, 9/15	18	5	19	27	16	25	38	7	34	36	9	1	28	37	42	43	44	5	26	17	39	13

In the case of Table 113, Equation 14 may be expressed as X₀=Y_π(0)=Y₂₂, X₁=Y_π(1)=Y₂₀, X₂=Y_π(2)=Y₇, . . . , X₄₃=Y_π(43)=Y₄₃, and X₄₄=Y_π(44)=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 22^nd group, the 1^st group to the 20^th group, the 2^nd group to the 7^th group, . . . , the 43^rd group to the 43^rd group, and the 44^th group to the 44^th group.

In the case of Table 114, Equation 14 may be expressed as X₀=Y_π(0)=Y₈, X₁=Y_π(1)=Y₄, X₂=Y_π(2)=Y₄₀, . . . , X₄₃=Y_π(43)=Y₃₉, and X₄₄=Y_π(44)=Y₁₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 8^th group, the 1^st group to the 4^th group, the 2^nd group to the 40^th group, . . . , the 43^rd group to the 39^th group, and the 44^th group to the 13^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 115 or 116 presented below:

TABLE 115
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	72	48	53	99	8	105	116	132	163	110	13	114
7/15,	81	62	161	145	140	100	102	45	7	18	76	15
8/15,	127	118	0	89	84	51	122	85	159	68	169	157
9/15	20	166	88	167	57	5	94	40	129	155	35	26
	156	3	143	165	170	24	136	121	93	144	29	58
	164	95	39	171	46	96	141	19	27	131	47	83
	9	151	28	43	138	113	130	124	142	147	69	117
	86	134	111	172	73	23	112	107	113	125	30	6
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	103	63	36	16	117	67	61	152	119	59	101
	7/15,	17	153	54	149	12	50	115	42	33	162	75
	8/15,	34	80	126	64	25	98	139	128	11	37	21
	9/15	14	52	74	92	71	41	135	79	106	173	97
		174	108	123	109	32	168	18	90	160	4	120
		82	31	77	70	41	148	146	60	87	78	150
		91	53	1	49	154	10	2	158	22	66	175
		65	56	104	176	177	178	179

TABLE 116
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15,	9	6	160	78	1	35	102	104	86	145	111	58
7/15,	32	139	42	40	105	100	144	115	154	136	97	135
8/15,	169	146	0	33	98	72	59	120	173	96	43	129
9/15	90	152	11	174	29	110	143	5	38	85	70	47
	107	66	171	130	65	3	17	37	121	18	113	51
	108	165	158	87	157	12	127	68	69	82	159	76
	23	172	91	71	61	126	60	103	149	84	118	39
	142	148	167	109	31	156	14	79	36	125	135	132
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15,	166	161	92	2	124	74	117	19	168	73	122
	7/15,	24	41	138	128	89	50	80	49	26	64	75
	8/15,	48	10	147	8	25	56	83	16	67	114	112
	9/15	133	94	53	99	162	27	170	163	57	131	34
		153	101	81	123	4	21	46	55	20	88	15
		54	157	119	140	93	106	62	95	164	141	150
		77	116	22	28	63	45	44	151	134	52	175
		30	7	13	176	177	178	179

In the case of Table 115, Equation 14 may be expressed as X₀=Y_π(0)=Y₇₂, X₁=Y_π(1)=Y₄₈, X₂=Y_π(2)=Y₅₅, . . . , X₁₇₈=Y_π(178)=Y₁₇₈, and X₁₇₉=Y_π(179)=Y₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 72^nd group, the 1^st group to the 48^th group, the 2^nd group to the 55^th group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In the case of Table 116, Equation 14 may be expressed as X₀=Y_π(0)=Y₉, X₁=Y_π(1)=Y₆, X₂=Y_π(2)=Y₁₆₀, . . . , X₁₇₈=Y_π(178)=Y₁₇₈, and X₁₇₉=Y_π(179)=Y₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 9^th group, the 1^st group to the 6^th group, the 2^nd group to the 160^th group, . . . , the 178^th group to the 178^th group, and the 179^th group to the 179^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 117 presented below:

TABLE 117
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
6/15	72	104	165	8	111	28	100	128	5	55	74	21
	96	177	82	178	66	16	56	146	179	120	47	144
	24	112	49	64	42	17	153	0	41	97	105	25
	145	81	1	123	83	60	53	69	157	159	91	87
	158	150	101	134	147	156	13	132	61	140	39	149
	19	71	52	99	34	15	143	127	124	102	46	7
	174	51	154	43	163	14	148	130	141	23	63	166
	79	171	44	4	90	115	107	164	125	27	131	3
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	6/15	75	170	152	40	162	129	168	122	85	114	176
		109	136	160	45	29	137	173	88	48	106	89
		80	73	57	65	161	9	121	169	113	33	32
		92	139	103	58	54	35	37	116	59	68	126
		108	50	10	67	22	30	142	167	138	110	6
		155	151	31	94	70	117	119	93	2	77	172
		86	16	125	84	11	62	133	36	76	12	135
		118	98	38	78	95	26	20

In the case of Table 117, Equation 14 may be expressed as X₀=Y_π(0)=Y₇₂, X₁=Y_π(1)=Y₁₀₄, X₂=Y_π(2)=Y₁₆₅, . . . , X₁₇₈=Y_π(178)=Y₂₆, and X₁₇₉=Y_π(179)=Y₂₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 72^nd group, the 1^st group to the 104^th group, the 2^nd group to the 165^th group, . . . , the 178^th group to the 26^th group, and the 179^th group to the 20^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 118 presented below:

TABLE 118
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
8/15	143	169	155	103	176	177	105	81	163	79	25	175
	43	115	75	69	53	35	131	99	51	117	21	13
	74	65	153	27	59	98	50	19	160	136	80	64
	24	137	0	171	147	48	33	18	128	3	58	73
	113	40	32	139	30	29	42	166	124	70	118	55
	138	94	167	111	162	90	173	23	76	110	95	135
	36	158	4	46	20	38	68	14	126	156	92	60
	119	109	101	66	146	52	116	134	84	71	7	37
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	8/15	41	129	67	157	178	57	179	107	93	85	133
		5	1	154	2	130	91	168	165	121	122	152
		72	88	89	161	17	11	144	83	34	26	97
		127	106	120	16	49	104	9	123	56	82	145
		8	164	102	39	44	62	10	45	100	174	132
		22	31	159	142	87	112	114	125	78	149	61
		151	141	150	86	15	170	108	47	28	54	77
		96	63	6	12	140	172	148

In the case of Table 118, Equation 14 may be expressed as X₀=Y_π(0)=Y₁₄₃, X₁=Y_π(1)=Y₁₆₉, X₂=Y_π(2)=Y₁₅₅, . . . , X₁₇₈=Y_π(178)=Y₁₇₂, and X₁₇₉=Y_π(179)=Y₁₄₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 143^rd group, the 1^st group to the 169^th group, the 2^nd group to the 155^th group, . . . , the 178^th group to the 172^nd group, and the 179^th group to the 148^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 119 presented below:

TABLE 119
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	43	21	51	14	129	106	84	155	169	143	118	100
	145	37	110	75	131	176	112	163	116	113	83	2
	58	36	4	24	98	96	60	154	144	33	19	107
	80	91	161	170	128	99	74	90	147	16	114	67
	122	49	18	138	56	64	41	146	3	9	66	152
	10	171	50	179	48	7	71	159	167	93	29	63
	70	78	95	23	15	94	111	134	62	79	13	141
	45	53	54	55	31	166	39	133	165	47	151	46
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	30	123	139	38	172	86	109	42	137	59	61
		130	97	162	153	1	92	57	73	160	40	25
		11	142	26	171	170	12	140	8	104	20	32
		27	85	177	35	178	68	89	115	168	105	82
		34	17	135	108	72	65	81	0	28	44	88
		135	173	174	22	156	132	69	149	87	148	103
		164	52	126	150	76	5	175	127	117	102	101
		6	77	119	125	124	157	158

In the case of Table 119, Equation 14 may be expressed as X₀=Y_π(0)=Y₄₃, X₁=Y_π(1)=Y₂₁, X₂=Y_π(2)=Y₅₁, . . . , X_r78=Y_π(178)=Y₁₅₇, and X₁₇₉=Y_π(179)=Y₁₅₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 43^rd group, the 1^st group to the 21^th group, the 2^nd group to the 51^st group, . . . , the 178^th group to the 157^th group, and the 179^th group to the 158^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 120 presented below:

TABLE 120
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
10/15	165	89	27	73	91	86	147	41	175	141	79	144
	35	176	177	40	178	24	179	169	72	32	42	76
	114	171	58	82	16	130	48	59	128	98	155	160
	153	96	154	2	123	11	145	112	84	90	131	119
	168	52	121	25	49	105	56	12	129	68	146	36
	139	97	120	9	113	167	166	71	134	102	23	15
	149	69	31	174	158	61	110	20	77	157	133	142
	85	111	159	100	7	13	126	54	37	78	109	5
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	10/15	46	6	53	407	135	104	65	30	1	19	143
		18	57	164	67	124	162	156	163	152	50	272
		60	88	148	92	75	161	8	81	64	34	136
		33	26	99	17	4	43	115	140	0	80	66
		3	51	106	137	122	10	83	170	74	138	28
		29	151	101	93	63	115	127	150	173	62	38
		94	132	21	39	95	87	118	125	44	45	70
		108	103	47	55	14	22	117

In the case of Table 120, Equation 14 may be expressed as X₀=Y_π(0)=Y₁₆₅, X₁=Y_π(1)=Y₈₉, X₂=Y_π(2)=Y₂₇, . . . , X₁₇₈=Y_π(178)=Y₂₂, and X₁₇₉=Y_π(179)=Y₁₁₇. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 165^th group, the 1^st group to the 89^th group, the 2^nd group to the 27^th group, . . . , the 178^th group to the 22^nd group, and the 179^th group to the 117^th group.

In another example, when the length N_ldpc of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 121 presented below:

TABLE 121
Code	Order of bits group to be block interleaved
Rate	π(j) (0 ≦ j < 180)
	0	1	2	3	4	5	6	7	8	9	10	11
	23	24	25	26	27	28	29	30	31	32	33	34
	46	47	48	49	50	51	52	53	54	55	56	57
	69	70	71	72	73	74	75	76	77	78	79	80
	92	93	94	95	96	97	98	99	100	101	102	103
	115	116	117	118	119	120	121	122	123	124	125	126
	138	139	140	141	142	143	144	145	146	147	148	149
	161	162	163	164	165	166	167	168	169	170	171	172
12/15	57	176	49	17	111	169	1	81	177	134	151	23
	97	87	179	88	125	154	83	34	29	75	59	139
	148	5	137	163	129	0	77	82	36	171	131	72
	13	128	33	172	133	67	2	76	149	64	69	115
	101	4	155	32	100	27	124	122	40	98	152	60
	160	168	138	89	48	114	68	8	108	43	21	104
	170	109	65	106	140	120	55	110	158	14	63	174
	22	46	119	54	30	166	102	6	156	150	94	71
	Code	Order of bits group to be block interleaved
	Rate	π(j) (0 ≦ j < 180)
		12	13	14	15	16	17	18	19	20	21	22
		35	36	37	38	39	40	41	42	43	44	45
		58	59	60	61	62	63	64	65	66	67	68
		81	82	83	84	85	86	87	88	89	90	91
		104	105	106	107	108	109	110	111	112	113	114
		127	128	129	130	131	132	133	134	135	136	137
		150	151	152	153	154	155	156	157	158	159	160
		173	174	175	176	177	178	179
	12/15	167	153	9	7	175	121	178	143	113	25	95
		105	45	66	35	144	44	173	10	141	84	42
		19	53	93	96	28	165	146	80	161	99	20
		52	132	37	92	90	51	74	130	147	61	16
		107	112	73	26	3	157	117	24	145	11	58
		123	91	18	56	164	136	85	41	162	12	50
		86	118	39	126	116	142	47	70	62	15	78
		135	127	38	31	159	79	103

In the case of Table 121, Equation 14 may be expressed as X₀=Y_π(0)=Y₅₇, X₁=Y_π(1)=Y₁₇₆, X₂=Y_π(2)=Y₄₉, . . . , X₁₇₈=Y_π(178)=Y₇₉, and X₁₇₉=_π(179)=Y₁₀₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^th group to the 57^th group, the 1^st group to the 176^th group, the 2^nd group to the 49^th group, . . . , the 178^th group to the 79^th group, and the 179^th group to the 103^rd group.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups in group units by using Equation 14 and Tables 107 to 121.

On the other hand, since the order of the groups constituting the LDPC codeword is rearranged in group units by the group interleaver 122, and then the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 107 to 121 in relation to π(j).

When the group interleaving is performed in the above-described method, the order of the groups constituting the group-interleaved LDPC codeword is different from that of exemplary embodiment 1.

This is because the block-row interleaver 125 is used in the present exemplary embodiment instead of the block interleaver 124 in FIG. 4. That is, since the interleaving method used in the block interleaver 124 and the interleaving method used in the block-row interleaver 125 are different from each other, the group interleaver 122 of the present exemplary embodiment rearranges the order of the plurality of groups constituting the LDPC codeword in a method different from that of exemplary embodiment 1.

Specifically, the group interleaver 122 may rearrange the order of the plurality of groups in such that that an arrangement unit, in which at least one group including bits to be mapped onto the same modulation symbol is serially arranged in group units, is repeated.

That is, the group interleaver 122 may serially arrange one of a plurality of first groups including bits to be mapped onto a first specific location of each modulation symbol, one of a plurality of second groups including bits to be mapped onto a second specific location of each modulation symbol, . . . , one of a plurality of n^th groups including bits to be mapped onto an n^th specific location of each modulation symbol, and may arrange the other groups repeatedly in the same method.

The block-row interleaver 125 interleaves the plurality of groups the order of which has been rearranged. In this case, the block-row interleaver 125 may interleave the plurality of groups the order of which has been rearranged in group units by using at least one row including a plurality of columns. This will be explained in detail below with reference to FIGS. 24 to 26.

FIGS. 24 to 26 are views to illustrate a configuration of a block-row interleaver and an interleaving method according to an exemplary embodiment.

First, when N_group/m is an integer, the block-row interleaver 125 includes an interleaver 125-1 including m number of rows each including M number of columns as shown in

FIG. 24, and the block-row interleaver 125 may interleave by using N_group/m number of interleavers 125-1 having the configuration of FIG. 24.

Herein, N_group is the total number of groups constituting an LDPC codeword. In addition, M is the number of bits included in a single group and may be 360, for example. m may be identical to the number of bits constituting a modulation symbol or may be 1/2 of the number of bits constituting a modulation symbol. For example, when a non-uniform QAM is used, performance of the bits constituting a modulation symbol is different, and thus, by setting m to be identical to the number of bits constituting a modulation symbol, a single group can be mapped onto a single bit of the modulation symbol.

Specifically, the block-row interleaver 125 may interleave by writing each of a plurality of groups constituting an LDPC codeword in each row in the row direction in group units, and reading each column of the plurality of rows in which the plurality of groups are written in group units in the column direction.

For example, as shown in FIG. 24, the block-row interleaver 125 writes m number of continuous groups from among the plurality of groups in each of the m number of rows of the interleaver 125-1 in the row direction, and reads each column of m number of rows in which bits are written in the column direction. In this case, as many interleavers 125-1 as the number of groups divided by the number of rows, that is, N_group/m, may be used.

As described above, when the number of groups constituting an LDPC codeword is an integer multiple of the number of rows, the block-row interleaver 125 may interleave by writing as many groups as the number of rows from among a plurality of groups constituting the LDPC codeword serially.

On the other hand, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of rows, the block-row interleaver 125 interleaves by using N number of interleavers (N is an integer greater than or equal to 2) including different number of columns.

For example, as shown in FIGS. 25 and 26, the block-row interleaver 125 may interleave by using a first interleaver 125-2 including m number of rows each including M number of columns, and a second interleaver 125-3 including m number of rows each including a×M Im number of columns. Herein, a is N_group−└N_group/m ┘×m, and └N_group/m┘ is the largest integer below N_group/m.

In this case, the first interleaver 125-2 may be used as many as └N_group/m┘ and one second interleaver 125-3 may be used.

Specifically, the block-row interleaver 125 may interleave a plurality of groups constituting an LDPC codeword by writing each of └N_group/m┘×m number of groups from among the plurality of groups constituting the LDPC codeword in each row in the row direction in group units, and reading each column of the plurality of rows in which └N_group/m ┘×m number of groups are written in group units in the column direction.

For example, as shown in FIGS. 25 and 26, the block-row interleaver 125 may write the same m number of continuous groups as the number of rows from among └N_group/m┘×m number of groups in each row of the first interleaver 125-2 in the row direction, and may read each column of the plurality of rows of the first interleaver 125-2 in which m number of groups are written in the column direction. In this case, the first interleaver 125-2 having the configuration FIGS. 25 and 26 may be used as many as └N_group/m┘.

In addition, in a system where a plurality of antennas are used, m may be the number of bits constituting a modulation method multiplied by the number of antennas.

Thereafter, the block-row interleaver 125 may divide bits included in the other groups except the groups written in the first interleaver 125-2, and may write these bits in each row of the second interleaver 125-3 in the row direction. In this case, the same number of bits are written in each row of the second interleaver 125-3. In other words, a single bit group may be input in a plurality of columns of the second interleaver 125-3.

For example, as shown in FIG. 25, the block-row interleaver 125 may write a×M Im number of bits from among the bits included in the other groups except the groups written in the first interleaver 125-2 in each of m number of rows of the second interleaver 125-3 in the row direction, and may read each column of m number of rows of the second interleaver 125-3 in which the bits are written in the column direction. In this case, one second interleaver 125-3 having the configuration of FIG. 25 may be used.

However, according to another exemplary embodiment, as shown in FIG. 26, the block-row interleaver 125 may write the bits in the first interleaver 125-2 in the same method as explained in FIG. 25, but may write the bits in the second interleaver 125-3 in a method different from that of FIG. 25.

That is, the block-row interleaver 125 may write the bits in the second interleaver 125-3 in the column direction.

For example, as shown in FIG. 26, the block-row interleaver 125 may write the bits included in the other groups except the groups written in the first interleaver 125-2 in each column of m number of rows each including a×M/m number of columns of the second interleaver 125-3 in the column direction, and may read each column of m number of rows of the second interleaver 125-3 in which the bits are written in the column direction. In this case, one second interleaver 125-3 having the configuration of FIG. 26 may be used.

In the method shown in FIG. 26, the block-row interleaver 125 interleaves by reading in the column direction after writing the bits in the second interleaver in the column direction. Accordingly, the bits included in the groups interleaved by the second interleaver are read in the order they were written and output to the modulator 130. Accordingly, the bits included in the groups belonging to the second interleaver are not rearranged by the block-row interleaver 125 and may be mapped onto the modulation symbols serially.

As described above, the block-row interleaver 125 may interleave the plurality of groups of the LDPC codeword by using the methods described above with reference to FIGS. 24 to 26.

According to the above-described method, the output of the block-row interleaver 125 may be the same as the output of the block interleaver 124. Specifically, when the block-row interleaver 125 interleaves as shown in FIG. 24, the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 8. In addition, when the block-row interleaver 125 interleaves as shown in FIG. 25, the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 9. In addition, when the block-row interleaver 125 interleaves as shown in FIG. 26, the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 10.

Specifically, when the group interleaver 122 is used based on Equation 11 and the block interleaver 124 is used, and the output groups of the group interleaver 122 are Y₁(0≦i<N_group) and when the group interleaver 122 is used based on Equation 13 and the block-row interleaver 125 is used, and the output groups of the group interleaver 122 are Z_i(0≦i<N_group), a relationship between the output groups Z_i and Y_i after group interleaving may be expressed as in Equations 15 and 16, and as a result, the same value may be output from the block interleaver 124:

Z _i+m×j =Y _α×i+j(0≦i<m,0≦j<α)  (15)

Z _i =Y _i(α×m≦i<N_group)  (16),

where α is └N_group/m┘ and is the number of groups written in a single column of the first part when the block interleaver 124 is used, and └N_group/m┘ is the largest integer below N_group/m. Here, m is identical to the number of bits constituting a modulation symbol or half of the bits constituting a modulation symbol. In addition, m is the number of columns of the block interleaver 124 and m is the number of rows of the block-row interleaver 125.

Accordingly, a case in which the group interleaving is performed by the group interleaver 122 based on Equation 11 and then the block interleaving is performed by the block interleaver 124, and a case in which the group interleaving is performed by the group interleaver 122 based on Equation 12 and then the block interleaving is performed by the block interleaver 124 may have an inverse relationship.

In addition, a case in which the group interleaving is performed by the group interleaver 122 based on Equation 13 and then the block-row interleaving is performed by the block-row interleaver 125, and a case in which the group interleaving is performed by the group interleaver 122 based on Equation 14 and then the block-row interleaving is performed by the block-row interleaver 125 may have an inverse relationship.

Accordingly, the modulator 130 may map the bits output from the block-row interleaver 125 onto a modulation symbol in the same method as when the block interleaver 124 is used.

The bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver 121, the group interleaver 122, the group twist interleaver 123, and the block interleaver 124 as shown in FIG. 4 (the parity interleaver 121 or the group twist interleaver 123 may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above.

For example, when the block interleaver is used and the group interleaving method expressed as in Equation 11 is used, regarding the bit groups X_j(0≦j<N_group) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X_π(1), X_(π(α+i), . . . , X_{π((m-1)×α+i)}} (0≦i<α), may constitute a single modulation symbol.

Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N_group/m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_i, {u_π(i)+j, u_π(α+i)+j, . . . , u_{π((m-1)×α+i)+j}} (0<i≦m, 0<j≦M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol.

In addition, the bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver 121, the group interleaver 122, the group twist interleaver 123, and the block-row interleaver 125 as shown in FIG. 23 (the group twist interleaver 123 may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above.

For example, when the block-row interleaver is used and the group interleaving method expressed as in Equation 13 is used, regarding the bit groups X_j(0≦j<N_group) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X_π(m×i), X_π(m×i+1), . . . , X_{π(m×i+(m-1))}} (0≦i<α), may constitute a single modulation symbol.

Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N_group/m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_i, {u_π(m×i)+j, u_π(m×i+1)+j, u_{π(m×i+(m+1))+j}} (0≦i<m, 0<j≦M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol.

Hereinafter, a method for determining π(j) which is a parameter used for group interleaving according to various exemplary embodiments will be explained.

Hereinafter, a method for designing the group interleaver 122 of FIG. 4 or 23 will be explained.

Criteria to be considered first are as follows:

Criteria 1) A different interleaving method is determined according to a modulation method and a code rate.

Criteria 2) A performance characteristic of LDPC codeword bits for each group and a performance characteristic of bits constituting a modulation signal should be considered simultaneously. For example, in the case of an LDPC codeword, the leftmost bits may have high performance, and the leftmost bits constituting the modulation symbol may have high performance. That is, regarding six (6) bits y₀, y₁, y₂, y₃, y₄, y₅ constituting the non-uniform 64-QAM, performance P(y_i) for each bit may have a relationship of P(y₀)>P(y₁)>P(y₂)>P(y₃)>P(y₄)>P(y₅).

Therefore, when a code of 64800 is used and the non-uniform 64-QAM (hereinafter, referred to as 64-NUQ) is used, it is determined which bit from among the six (6) bits of 64-NUQ is mapped with 180 LDPC groups, considering characteristics of the LDPC code and the modulation method simultaneously, and a case of the highest estimated performance is determined by using a density evolution method.

That is, many cases in which 180 groups can be mapped onto the six (6) bits are considered, and a theoretically estimated threshold value for each case is calculated by the density evolution method. Herein, the threshold is an SNR value and an error probability is “0” in an SNR region higher than the threshold value when the LDPC codeword is transmitted. Therefore, when the LDPC codeword is transmitted in a method of the case in which the threshold value is small from among many cases for mapping, high performance can be guaranteed. Designing an interleaver based on the density evolution is a theoretical approach. Therefore, an interleaver should be designed by verifying code performance based on an actually designed parity check matrix and based on cycle distribution, as well as the theoretical approach of the density evolution.

Herein, considering the many cases in which 180 groups can be mapped onto the six (6) bits refers to re-grouping the groups into groups related to the rows of the same degree of the parity check matrix and considering how many groups will be mapped onto the six (6) 64 QAM bits.

Hereinafter, a case where 256-QAM is used will be described in detail.

In case of a LDPC codeword, leftmost bits have superior performance, and the performance of the bits forming a modulation symbol and leftmost bits may be superior. In other words, as for eight bits constituting non-uniform 256-QAM, y₀, y₁, y₂, y₃, y₄, y₅, y₆, y₇, the performance of each bit P(y_i) becomes P(y₀)>P(y₁)>P(y₂)>P(y₃)>P(y₄)>P(y₅)>P(y₆)>P(y₇) In addition, if a code rate is 12/15, there are 26 bit groups corresponding to the column group of which degree is 14 in the parity check matrix, 118 bit groups corresponding to the column group of which degree is 3 in the parity check matrix, and 36 bit groups corresponding to the column group of which degree is 2 in the parity check column, among 180 LDPC codeword bit groups.

As a result of using a density evolution method, there are 26 bit groups corresponding to the column group of which degree is 14 in the parity check matrix, as for the bit groups X_j(0≦j<25) which are defined as shown in Equations 9 and 10, there are 12 groups mapping onto y₁, 1 group mapped onto y₆, and 9 groups mapped onto y₇.

In addition, there are 118 bit groups corresponding to the column group of which degree is 3 in the parity check matrix, as for the bit groups X_j(26≦j<143) which are defined as shown in Equations 9 and 10, there are 22 groups mapping onto y₀, 10 groups mapped onto y₁, 22 groups mapped onto y₂, 22 groups mapped onto y₃, 20 groups mapped onto y₄, and 22 groups mapped onto y₅

Further, there are 36 bit groups corresponding to the column group of which degree is 2 in the parity check matrix, as for the bit groups X_j(144≦j<180) which are defined as shown in Equations 9 and 10, there are 2 groups mapped onto y₄, 21 groups mapped onto y₆, and 13 groups mapped onto y₇.

In this case, the LDPC codeword bit groups which are input and mapped onto the second part of the block interleaver 124 or the second interleaver 125-3 of the block-row interleaver 125 may guarantee the most superior performance when there are four bit groups among the bit groups corresponding to the column group of which degree is 14 in the parity check matrix.

The summary of the above-mentioned contents may be represented as shown in the following table 122.

	TABLE 122
	y0	y1	y2	y3	y4	y5	y6	y7	Sum
Degree 14 (a)	0	12	0	0	0	0	1	9	22
Degree 3 (b)	22	10	22	22	20	22	0	0	118
Degree 2 (c)	0	0	0	0	2	0	21	13	36
Sum (a + b + c)	22	22	22	22	22	22	22	22

In other words, in table 41, 22 bit groups {51, 122, 91, 111, 95, 100, 119, 130, 78, 57, 65, 26, 61, 126, 105, 143, 70, 132, 39, 102, 115, 116} are mapped onto y₀, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3 in the parity check matrix. The selected bit groups optimize actual BER/FER performance.

In addition, 22 bit groups {6, 14, 3, 21, 71, 134, 2, 0, 140, 106, 7, 118, 23, 35, 20, 17, 50, 48, 112, 13, 66, 5} are mapped onto y₁, and 12 bit groups are selected from the bit groups corresponding to the column group of which degree is 14, and 10 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

Further, 22 bit groups {75, 42, 129, 107, 30, 45, 137, 114, 37, 87, 53, 85, 101, 141, 120, 99, 88, 117, 64, 28, 135, 138} are mapped onto y₂, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

In addition, 22 bit groups {108, 113, 58, 97, 38, 124, 86, 33, 74, 32, 29, 128, 67, 104, 80, 127, 56, 34, 89, 94, 49, 55} are mapped onto y₃ and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

Further, 22 bit groups {93, 136, 68, 62, 54, 40, 81, 103, 121, 76, 44, 84, 96, 123, 154, 98, 82, 142, 46, 169, 131, 72} are mapped onto y₄, and 20 bit groups are selected from the bit groups corresponding to the column group of which degree is 3, and 2 bit groups are selected from the bit groups corresponding to the column group of which degree is 2.

In addition, 22 bit groups {47, 69, 125, 31, 83, 36, 59, 90, 79, 52, 133, 60, 92, 139, 110, 27, 73, 43, 77, 109, 63, 41} are mapped onto y₅, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

Further, 22 bit groups {168, 147, 161, 165, 175, 162, 164, 158, 157, 160, 150, 171, 167, 145, 151, 153, 9, 155, 170, 146, 166, 149} are mapped onto y₆, and one bit group is selected from the bit groups corresponding to the column group of which degree is 14, and 21 bit groups are selected from the bit groups corresponding to the column group of which degree is 2.

In addition, 22 bit groups {15, 159, 11, 176, 152, 156, 144, 148, 172, 178, 24, 22, 179, 4, 163, 174, 173, 19, 10, 177, 12, 16} are mapped onto y₇, and 9 bit groups are selected from the bit groups corresponding to the column group of which degree is 14, and 13 bit groups are selected from the bit groups corresponding to the column group of which degree is 2.

Further, 4 bit groups {1, 8, 18, 25} are selected from the bit groups corresponding to the column group of which degree is 14, and the bit groups are input to the second part of the block interleaver or the second interleaver of the block-row interleaver. The bit group X₁ is mapped onto y₀ or y₁, the bit group X₈ is mapped onto y₂ or y₃, the bit group X₁₈ is mapped onto y₄ or y₅, and the bit group X₂₅ is mapped onto y₆ or y₇.

In the above-described method, the group interleaver 122 of FIG. 4 or 23 may be designed.

FIG. 27 is a block diagram to illustrate a configuration of a receiver apparatus according to an exemplary embodiment. Referring to FIG. 27, the receiver apparatus 2700 includes a demodulator 2710, a multiplexer 2720, a deinterleaver 2730 and a decoder 2740.

The demodulator 2710 receives and demodulates a signal transmitted from the transmitter apparatus 100. Specifically, the demodulator 2710 generates a value corresponding to an LDPC codeword by demodulating the received signal, and outputs the value to the multiplexer 2720. In this case, the demodulator 2710 may use a demodulation method corresponding to a modulation method used in the transmitter apparatus 100.

The value corresponding to the LDPC codeword may be expressed as a channel value for the received signal. There are various methods for determining the channel value, and for example, a method for determining a Log Likelihood Ratio (LLR) value may be the method for determining the channel value.

The LLR value is a log value for a ratio of the probability that a bit transmitted from the transmitter apparatus 100 is 0 and the probability that the bit is 1. In addition, the LLR value may be a bit value which is determined by a hard decision, or may be a representative value which is determined according to a section to which the probability that the bit transmitted from the transmitter apparatus 100 is 0 or 1 belongs.

The multiplexer 2720 multiplexes the output value of the demodulator 2710 and outputs the value to the deinterleaver 2730.

Specifically, the multiplexer 2720 is an element corresponding to a demultiplexer such as the demultiplexer shown in FIG. 12 or 13 provided in the transmitter apparatus 100, and performs an operation corresponding to the demultiplexer. Accordingly, when the demultiplexer is omitted from the transmitter apparatus 100, the multiplexer 2720 may be omitted from the receiver apparatus 2700.

That is, the multiplexer 2720 converts the output value of the demodulator 2710 into cell-to-bit and outputs an LLR value on a bit basis.

In this case, when the demultiplexer does not change the order of the LDPC codeword bits as shown in FIG. 13, the multiplexer 2720 may output the LLR values serially on the bit basis without changing the order of the LLR values corresponding to the bits of the cell. Alternatively, the multiplexer 2720 may rearrange the order of the LLR values corresponding to the bits of the cell to perform an inverse operation to the demultiplexing operation of the demultiplexer based on Table 50.

The deinterleaver 2730 deinterleaves the output value of the multiplexer 2720 and outputs the values to the decoder 2740.

Specifically, the deinterleaver 2730 is an element corresponding to the interleaver 120 of the transmitter apparatus 100 and performs an operation corresponding to the interleaver 120. That is, the deinterleaver 2730 deinterleaves the LLR value by performing the interleaving operation of the interleaver 120 inversely.

In this case, the deinterleaver 2730 may include elements as shown in FIG. 28 or 29.

First, as shown in FIG. 28, the deinterleaver 2730 includes a block deinterleaver 2731, a group twist deinterleaver 2732, a group deinterleaver 2733, and a parity deinterleaver 2734, according to an exemplary embodiment.

The block deinterleaver 2731 deinterleaves the output of the multiplexer 2720 and outputs a value to the group twist deinterleaver 2732.

Specifically, the block deinterleaver 2731 is an element corresponding to the block interleaver 124 provided in the transmitter apparatus 100 and performs the interleaving operation of the block interleaver 124 inversely.

That is, the block deinterleaver 2731 deinterleaves by using at least one row formed of a plurality of columns, that is, by writing the LLR value output from the multiplexer 2720 in each row in the row direction and reading each column of the plurality of rows in which the LLR value is written in the column direction.

In this case, when the block interleaver 124 interleaves by dividing a column into two parts, the block deinterleaver 2731 may deinterleave by dividing a row into two parts.

In addition, when the block interleaver 124 performs writing and reading with respect to a group which does not belong to the first part in the row direction, the block deinterleaver 2731 may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the row direction.

Hereinafter, the block deinterleaver 2731 will be described with reference to FIG. 31. However, this is only an example, and the block deinterleaver 2731 may be realized in other methods.

Input LLR v_i(0≦i<N_ldpc) is written in row r_i column c_i of the block deinterleaver 2731. Herein, c_i=(i mod N_c), r_i=└i/N_c┘.

Meanwhile, output LLR q_i(0≦i<N_c×N_r1) is led from row c_i, column r₁ of the first part of the block deinterleaver 2731. Herein, r_i=(i mod N_r1), c_i=└i/N_r1┘.

In addition, output LLR q_i(N_c×N_r1≦i<N_ldpc) is led from row c_i column r_i of the second part of the block deinterleaver 2731. Herein, r_i=N_r1+{(i−N_c×N_r1) mod N_r2}, c_i=└(1−N_c×N_r1)/N_r2┘.

The group twist deinterleaver 2732 deinterleaves the output value of the block deinterleaver 2731 and outputs the value to the group deinterleaver 2733.

Specifically, the group twist deinterleaver 2732 is an element corresponding to the group twist interleaver 123 provided in the transmitter apparatus 100, and may perform the interleaving operation of the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 2732 may rearrange the LLR values of the same group by changing the order of the LLR values existing in the same group. When the group twist operation is not performed in the transmitter apparatus 100, the group twist deinterleaver 2732 may be omitted.

The group deinterleaver 2733 (or the group-wise deinterleaver) deinterleaves an output value of the group twist deinterleaver 2732 and outputs a value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element corresponding to the group interleaver 122 provided in the transmitter apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units. In this case, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units by applying the interleaving method of Tables 27 to 56 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

As described above, it is possible to rearrange the order of column groups in the parity check matrix having the shape of FIGS. 2 and 3, and a column group corresponds to a bit group. Accordingly, if the order of column groups is changed in the parity check matrix, the order of bit groups may also be changed and the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units accordingly.

The parity deinterleaver 2734 performs parity deinterleaving with respect to an output value of the group deinterleaver 2733 and outputs a value to the decoder 2740.

Specifically, the parity deinterleaver 2734 is an element corresponding to the parity interleaver 121 provided in the transmitter apparatus 100 and may perform the interleaving operation of the parity interleaver 121 inversely. That is, the parity deinterleaver 2734 may deinterleave the LLR values corresponding to the parity bits from among the LLR values output from the group deinterleaver 2733. In this case, the parity deinterleaver 2734 may deinterleave the LLR values corresponding to the parity bits in an inverse method of the parity interleaving method of Equation 8.

However, the parity deinterleaving is performed only when the transmitter apparatus 100 generates the LDPC codeword using the parity check matrix 200 as shown in FIG. 2. The parity deinterleaver 2734 may be omitted when the LDPC codeword is encoded based on the parity check matrix 300 as shown in FIG. 3. However, even when the LDPC codeword is generated using the parity check matrix 200 of FIG. 2, LDPC decoding may be performed based on the parity check matrix 300 of FIG. 3, and in this case, the parity deinterleaver 2734 may be omitted.

Although the deinterleaver 2730 of FIG. 27 includes three (3) or four (4) elements as shown in FIG. 28, operations of the elements may be performed by a single element. For example, when bits each of which belongs to each of bit groups Xa, Xb, Xc, and Xd constitute a single modulation symbol, the deinterleaver may deinterleave these bits to locations corresponding to their bit groups based on the received single modulation symbol.

For example, if the code rate is 12/15, and the modulation method is 256-QAM, the group deinterleaver 2733 may perform deinterleaving based on Table 41, and in this case, one bit from each of the bit groups X₅₁, X₆, X₇₅, X₁₀₈, X₉₃, X₄₇, X₁₆₈, X₁₅ constitutes a single modulation symbol. Therefore, the deinterleaver 2730 may perform mapping with the decoded initial value corresponding to the bit groups X₅₁, X₆, X₇₅, X₁₀₈, X₉₃, X₄₇, X₁₆₈, X₁₅ based on the received modulation symbol.

The deinterleaver 2730 may include a block-row deinterleaver 2735, a group twist deinterleaver 2732, a group deinterleaver 2733 and a parity deinterleaver 2734, as shown in FIG. 29. In this case, the group twist deinterleaver 2732 and the parity deinterleaver 2734 perform the same functions as in FIG. 27, and thus, a redundant explanation is omitted.

The block-row deinterleaver 2735 deinterleaves an output value of the multiplexer 2720 and outputs a value to the group twist deinterleaver 2732.

Specifically, the block-row deinterleaver 2735 is an element corresponding to the block-row interleaver 125 provided in the transmitter apparatus 100 and may perform the interleaving operation of the block-row interleaver 125 inversely.

That is, the block-row deinterleaver 2735 may deinterleave by using at least one column formed of a plurality of rows, that is, by writing the LLR values output from the multiplexer 2720 in each column in the column direction and reading each row of the plurality of columns in which the LLR value is written in the column direction.

However, when the block-row interleaver 125 performs writing and reading with respect to a group which does not belong to the first part in the column direction, the block-row deinterleaver 2735 may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the column direction.

The group deinterleaver 2733 deinterleaves the output value of the group twist deinterleaver 2732 and outputs the value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element corresponding to the group interleaver 122 provided in the transmitter apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units. In this case, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units by applying the interleaving method of Tables 92 to 121 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

Meanwhile, the deinterleaver 2730 of FIG. 27 may consisted of 3 or 4 elements as shown in FIG. 29, but the operation of elements may be performed as one element. For example, if one bit which belongs to each of bit groups Xa, Xb, Xc, Xd consists of a single modulation symbol, the deinterleaver 2730 may perform deinterleaving at a location corresponding to the bit groups based on the received modulation symbol.

In addition, when transmission is performed from a transmitter based on a block interleaver, a receiver may operate by determining the deinterleaving order in the deinterleaver 2835 based on Equations 15 and 16. In addition, when transmission is performed based on a block-row interleaver from a transmitter, the receiver may operate by determining the interleaving order in the block deinterleaver 2731 based on Equations 15 and 16.

The decoder 2740 may perform LDPC decoding by using the output value of the deinterleaver 2730. To achieve this, the decoder 2740 may include a separate LDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 2740 is an element corresponding to the encoder 110 of the transmitter apparatus 200 and may correct an error by performing the LDPC decoding by using the LLR value output from the deinterleaver 2730.

For example, the decoder 2740 may perform the LDPC decoding in an iterative decoding method based on a sum-product algorithm. The sum-product algorithm is one example of a message passing algorithm, and the message passing algorithm refers to an algorithm which exchanges messages (e.g., LLR value) through an edge on a bipartite graph, calculates an output message from messages input to variable nodes or check nodes, and updates.

The decoder 2740 may use a parity check matrix when performing the LDPC decoding. In this case, an information word submatrix in the parity check matrix is defined as in Tables 4 to 26 according to a code rate and a length of the LDPC codeword, and a parity submatrix may have a dual diagonal configuration.

In addition, information on the parity check matrix and information on the code rate, etc. which are used in the LDPC decoding may be pre-stored in the receiver apparatus 2700 or may be provided by the transmitter apparatus 100.

FIG. 30 is a flowchart to illustrate a signal processing method of a transmitter apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by performing LDPC encoding (S3010). In this case, when the LDPC encoding is performed, a parity check matrix including an information word submatrix defined by Tables 4 to 26 and a parity submatrix having a dual diagonal configuration (that is, the parity check matrix as shown in FIG. 2) may be used, or a parity check matrix which is obtained by row and column permutating the parity check matrix of FIG. 2 based on Equation 4 and Equation 5 (that is, the parity check matrix as shown in FIG. 3).

Thereafter, the LDPC codeword is interleaved (S3020).

The interleaved LDPC codeword is mapped onto a modulation symbol (S3030). In this case, a bit included in a predetermined group from among a plurality of groups of the LDPC codeword may be mapped onto a predetermined bit of the modulation symbol.

Herein, each of the plurality of groups may be formed of 360 bits.

In operation S3020, parity bits of the LDPC codeword may be interleaved, the parity-interleaved LDPC codeword may be divided into a plurality of groups, the order of the plurality of groups may be rearranged in group units, and the plurality of groups the order of which has been rearranged may be interleaved.

Specifically, the order of the plurality of groups may be rearranged in group units based on Equation 11 described above. In this case, π(j) of Equation 11 may be determined based on at least one of a length of the LDPC codeword, a modulation method and a code rate.

For example, π(j) may be defined as in Table 37 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15.

In another example, π(j) may be defined as in Table 38 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15.

In another example, π(j) may be defined as in Table 39 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

In another example, π(j) may be defined as in Table 40 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

In another example, π(j) may be defined as in Table 41 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15.

However, these are merely examples. π(j) may be defined as in Tables 27 to 36 according to the length of the LDPC codeword, the modulation method and the code rate.

In addition, Equation 12 may be used in rearranging the order of the plurality of groups in group units. In this case, π(j) may be defined as in Tables 42 to 56 described above.

The plurality of groups the order of which has been rearranged may be interleaved by writing the plurality of groups in each of the plurality of columns in the column direction in group units, and reading each row of the plurality of columns in which the plurality of groups are written in group units in the row direction.

In this case, from among the plurality of groups, at least some group which can be written in each of the plurality of columns in group units is written in each of the plurality of columns serially, and then, the other groups are divided and written in the other areas which remain in each of the plurality of columns after the at least some group has been written in group units.

In addition, the order of the plurality of groups is rearranged in group units such that groups including bits to be mapped onto the same location of different modulation symbols are serially arranged to be adjacent to one another, and the predetermined group is written in a predetermined column.

In this case, in operation S3030, a modulation symbol may be generated by mapping bits output from the predetermined column onto a predetermined bit of each modulation symbol.

In operation S3020, the interleaving may be performed in other methods in addition to the above-described method.

Specifically, the interleaving may be performed by using Equation 13 and Tables 92 to 106 described above, or may be performed by using Equation 14 and Tables 107 to 121 described above.

In these cases, the order of the plurality of groups may be rearranged in group units such that an arrangement unit, in which groups including bits to be mapped onto the same modulation symbol are serially arranged in group units, is repeated.

When a plurality of groups are interleaved, this interleaving may be performed by writing in each row at least one group including bits to be mapped onto a same modulation symbol from among the plurality of groups the order of which has been rearranged in the row direction, and reading each column of the row in which the at least one group is written in the column direction.

A non-transitory computer readable medium, which stores a program for performing the above signal processing methods according to various exemplary embodiments in sequence, may be provided.

The non-transitory computer readable medium refers to a medium that stores data semi-permanently rather than storing data for a very short time, such as a register, a cache, and a memory, and is readable by an apparatus. Specifically, the above-described various applications or programs may be stored in a non-transitory computer readable medium such as a compact disc (CD), a digital versatile disk (DVD), a hard disk, a Blu-ray disk, a universal serial bus (USB), a memory card, and a read only memory (ROM), and may be provided.

Components, elements or units represented by a block as illustrated in FIGS. 1, 4, 12, 13, 23 and 27-29 may be embodied as the various numbers of hardware, software and/or firmware structures that execute respective functions described above, according to exemplary embodiments. For example, these components, elements or units may use a direct circuit structure, such as a memory, processing, logic, a look-up table, etc. that may execute the respective functions through controls of one or more microprocessors or other control apparatuses. These components, elements or units may be specifically embodied by a module, a program, or a part of code, which contains one or more executable instructions for performing specified logic functions. Also, at least one of the above components, elements or units may further include a processor such as a central processing unit (CPU) that performs the respective functions, a microprocessor, or the like.

Although a bus is not illustrated in the block diagrams of the transmitter apparatus and the receiver apparatus, communication may be performed between each element of each apparatus via the bus. In addition, each apparatus may further include a processor such as a Central Processing Unit (CPU) or a microprocessor to perform the above-described various operations.

The foregoing exemplary embodiments and advantages are merely exemplary and are not to be construed as limiting the present inventive concept. The exemplary embodiments can be readily applied to other types of apparatuses. Also, the description of the exemplary embodiments is intended to be illustrative, and not to limit the scope of the inventive concept, and many alternatives, modifications, and variations will be apparent to those skilled in the art.

Claims

1. An interleaving method of a transmitter, the interleaving method comprising: encoding input bits to generate parity bits;interleaving a Low Density Parity Check (LDPC) codeword comprising the input bits and the parity bits; andmapping the interleaved LDPC codeword onto a plurality of constellation points, wherein the interleaving comprises:interleaving the parity bits;splitting the interleaved LDPC codeword comprising the input bits and the interleaved parity bits into a plurality of bit groups;interleaving the plurality of bit groups; andinterleaving the interleaved plurality of bit groups.

2. The method of claim 1, wherein each of the plurality of bit groups comprises 360 bits.

3. The method of claim 1, wherein the interleaving the plurality of bit groups comprises interleaving the plurality of bit groups using the following equation: Yj=Xπ(j)(0≦j<Ngroup)where Xj is a j-th bit group among the plurality of bit groups, Yj is an interleaved j-th bit group, Ngroup is a total number of the plurality of bit groups, and π(j) denotes a permutation order for group-wise interleaving.

4. The method of claim 3, wherein π(j) is determined based on at least one of a code length of the LDPC codeword, a modulation method and a code rate.

5. The method of claim 3, wherein π(j) is defined as a table below when a code length of the LDPC codeword is 64800, a modulation method is 256-QAM, and a code rate is 12/15: