Patent Grant
11824558
Apparatuses and methods consistent with the exemplary embodiments of the inventive concept relate to encoding and decoding Low Density Parity Check (LDPC) codes, and more particularly, to encoding and decoding LDPC codes which perform LDPC encoding and decoding based on a parity-check matrix.
In a communication/broadcasting system, link performance may considerably deteriorate due to various types of noises, a fading phenomenon, and inter-symbol interference (ISI) of a channel. Therefore, to implement high-speed digital communication/broadcasting systems requiring high data throughput and reliability like next-generation mobile communications, digital broadcasting, and portable Internet, it has been required to develop technologies to overcome the noises, the fading, and the inter-symbol interference. As part of studies to overcome the noises, etc., a study on an error-correcting code which is a method for increasing reliability of communications by efficiently recovering distorted information has been actively conducted recently.
LDPC codes which were first introduced by Gallager in the 1960s remain forgotten for a very long time due to complexity which could hardly be implemented at the technology level at that time. However, as performance of turbo codes proposed by Berrou, Glavieux, and Thitimajshima in 1993 approaches Shannon's channel capacity, many studies on channel encoding based on iterative decoding and a graph thereof by performing many different interpretations on performance and characteristics of the turbo codes have been conducted. As a result, as the LDPC codes in the late 1990s are restudied, when the LDPC codes are decoded by applying sum-product algorithm based iterative decoding to the LDPC codes on a tanner graph corresponding to the LDPC codes, it was found that the performance of the LDPC codes approaches the Shannon's channel capacity.
The LDPC codes may be generally defined by a parity-check matrix and represented using a bipartite graph commonly referred to as the tanner graph.
Hereinafter, a systematic LDPC codeword will be described with reference to
The LDPC codes are a kind of linear block codes and include a process of determining a codeword satisfying conditions of following mathematical expression 1.
H·cT=[h0,h1,h2, . . . ,hN
where C=[c0, c1, c2, . . . , cN
In mathematical expression 1 above, H represents the parity-check matrix, C represents the codeword, ci represents an i-th bit of the codeword, and Nldpc represents a codeword length. Here, hi represents an i-th column of the parity-check matrix H.
The parity-check matrix H is formed of the same Nldpc columns as the number of bits of the LDPC codeword. The mathematical expression 1 represents that since a sum of a product of the i-th column hi of the parity-check matrix and the i-th bit ci of the codeword becomes “0”, the i-th column hi has a relationship with the i-th bit ci of the codeword.
Meanwhile, the performance of the LDPC codes may be determined according to the parity-check matrix. Therefore, there is a need to design the parity-check matrix for the LDPC codes having improved performance.
One or more exemplary embodiments may overcome the above disadvantages and other disadvantages not described above. However, these embodiments 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 method and an apparatus for encoding and decoding LDPC codes capable of improving LDPC encoding and decoding performance.
According to an aspect of an exemplary embodiment, there is provided an encoding apparatus which may include: an LDPC encoder configured to perform LDPC encoding on input bits based on a first parity-check matrix or a second parity-check matrix to generate an LDPC codeword formed of 64,800 bits, wherein the parity-check matrix includes an information word sub-matrix and a parity sub-matrix, and the information word sub-matrix is formed of a plurality of column blocks each including 360 columns, and is defined by a table which represents positions of value one (1) presented in every 360-th column.
The LDPC encoder may perform the LDPC encoding using a parity-check matrix defined by a table like Table 17 when a code rate is 6/15.
The LDPC encoder may perform the LDPC encoding using a parity-check matrix defined by a table like Table 14 when the code rate is 8/15.
The LDPC encoder may perform the LDPC encoding using a parity-check matrix defined by a table like Table 18 when the code rate is 10/15.
The LDPC encoder may perform the LDPC encoding using a parity-check matrix defined by a table like Table 16 when the code rate is 12/15.
According to an aspect of another exemplary embodiment, there is provided an encoding method which may include: generating an LDPC codeword formed of 64,800 bits by performing LDPC encoding on input bits based on a parity-check matrix, in which the parity-check matrix includes an information word sub-matrix and a parity sub-matrix and the information word sub-matrix is formed of a plurality of column blocks each including 360 columns, and is defined by a table which represents positions of value one (1) presented in every 360-th column.
In the generating the LDPC codeword, the LDPC encoding may be performed using a parity-check matrix defined by a table like Table 17 when a code rate is 6/15.
In the generating of the LDPC codeword, the LDPC encoding may be performed using a parity-check matrix defined by a table like Table 14 when the code rate is 8/15.
In the generating the LDPC codeword, the LDPC encoding may be performed using a parity-check matrix defined by a table like Table 18 when the code rate is 10/15.
In the generating the LDPC codeword, the LDPC encoding may be performed using a parity-check matrix defined by a table like Table 16 when the code rate is 12/15.
According to an aspect of still another exemplary embodiment, there is provided a decoding apparatus which may include: an LDPC decoder configured to perform LDPC decoding on an LDPC codeword formed of 64,800 bits based on a parity-check matrix, wherein the parity-check matrix includes an information word sub-matrix and a parity sub-matrix, and the information word sub-matrix is formed of a plurality of column blocks each including 360 columns, and is defined by a table which represents positions of value one (1) presented in every 360-th column.
The LDPC decoder may perform the LDPC decoding using a parity-check matrix defined by a table like Table 17 when the code rate is 6/15.
The LDPC decoder may perform the LDPC decoding using a parity-check matrix defined by a table like Table 14 when the code rate is 8/15.
The LDPC decoder may perform the LDPC decoding using a parity-check matrix defined by a table like Table 18 when the code rate is 10/15.
The LDPC decoder may perform the LDPC decoding using a parity-check matrix defined by a table like Table 16 when the code rate is 12/15.
According to an aspect of still another exemplary embodiment, there is provided a decoding method which may include: performing LDPC decoding on an LDPC codeword formed of 64,800 bits based on a parity-check matrix, in which the parity-check matrix includes an information word sub-matrix and a parity sub-matrix and the information word sub-matrix is formed of a plurality of column blocks each including 360 columns, and is defined by a table which represents positions of value one (1) present in every 360-th column.
In the performing the LDPC decoding, the LDPC decoding may be performed using a parity-check matrix defined by a table like Table 17 when the code rate is 6/15.
In the performing the LDPC decoding, the LDPC decoding may be performed using a parity-check matrix defined by a table like Table 14 when the code rate is 8/15.
In the performing the LDPC decoding, the LDPC decoding may be performed using a parity-check matrix defined by a table like Table 18 when the code rate is 10/15.
In the performing the LDPC decoding, the LDPC decoding may be performed using a parity-check matrix defined by a table like Table 16 when the code rate is 12/15.
Additional and/or other aspects and advantages of the exemplary embodiments will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of these embodiments.
The above and/or other aspects will be more apparent by describing certain exemplary embodiments with reference to the accompanying drawings, in which:
Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings. Further, in describing the exemplary embodiments, detailed descriptions of well-known functions or constructions will be omitted so as not to obscure the description with unnecessary detail.
Hereinafter, the exemplary embodiments will describe a technology of LDPC encoding and LDPC decoding in a communication/broadcasting system.
Hereinafter, the exemplary embodiments use terms and names which are defined in the Digital Video Broadcasting the Second Generation Terrestrial (DVB-T2) system which is one of the European digital broadcasting standards and North America digital broadcasting standard system, Advanced Television Systems Committee (ATSC) 3.0 which is being established as standard. However, the inventive concept is not limited to these terms and names, but may be similarly applied to other systems.
A graph representation method of LDPC codes will be described with reference to
Referring to
A degree of the variable node and the check node on the tanner graph of the LDPC codes represents the number of edges connected to each node, which is the same as the number of non-zero entries in a row or a column corresponding to the corresponding node in the parity-check matrix of the LDPC codes. For example, in
The LDPC codes may be decoded using an iterative decoding algorithm based on a sum-product algorithm on a bipartite graph illustrated in
Herein, a value of an i-th encoding bit may be determined based on a message of an i-th variable node. A soft decision and a hard decision may be performed on the value of the i-th encoding bit. Therefore, performance of an i-th bit ci of the LDPC codeword corresponds to performance of the i-th variable node, which may be determined depending on positions and the number of ones (1s) in the i-th column of the parity-check matrix. That is, performance of Nldpc bits of the codeword relies on the positions and number of ones (1s) in the parity-check matrix.
Hereinafter, characteristics of the parity-check matrix of the LDPC codes having a specific structure will be described with reference to
In
Referring to
Positions of entries having weight-1s, that is, value one (1) present in the parity sub-matrix 320 including a Kldpc-th column to an (Nldpc−1)-th column of the parity-check matrix 300 have a dual diagonal structure. Therefore, among the columns included in the parity sub-matrix 320, all the degrees (herein, the degree is the number of ones (1s) included in each column) of the remaining columns except the (Nldpc−1)-th column are two (2) and the degree of the (Nldpc−1)-th column is one (1).
Meanwhile, a structure of the information word sub-matrix 310, that is, the sub-matrix including a zero (0)-th column to a (Kldpc−1)-th column depends on the following rule.
First, the Kldpc columns corresponding to the information word in the parity-check matrix 300 belong to a plurality of column groups each having M columns, and the information word sub-matrix 310 is divided into a total of Kldpc/M column groups. In columns belonging to the same column group, positions of rows at which one (1) is present have a relationship in which a row having a value of one (1) is shifted by Qldpc from an immediately previous row having the same value of one (1). Here, Qldpc may be an integer greater than or equal to one (1).
Second, if it is assumed that a degree of a zero (0)-th column of an i-th (i=0, 1, . . . , Kldpc/M−1) column group is Di and positions of each row at which one (1) is positioned are Ri,0(0), Ri,o(1), . . . , R0(D
Ri,j(k)=(Ri,(j−1)(k)+Qldpc)mod(Nldpc−Kldpc) (2)
In mathematical expression 2 above, k=0, 1, 2, . . . , Di−1, i=0, 1, . . . , Kldpc/M−1, and j=1, 2, . . . , M−1.
The above mathematical expression 2 may be represented like following mathematical expression 3.
Ri,j(k)=(R1,0(k)+(j mod M)×Qldpc)mod(Nldpc−Kldpc) (3)
In mathematical expression 3 above, k=0, 1, 2, . . . , Di−1, i=0, 1, . . . , Kldpc/M−1, and j=1, 2, . . . , M−1.
In the above mathematical expressions, Ri,j(k) represent the indices of the row at which the k-th weight-1 is positioned in the j-th column of the i-th column group, Nldpc represents the LDPC codeword length, Kldpc represents the information word length, Di represents the degree of a zero (0)-th column belonging to the i-th column group, and M represents the number of columns belonging to one column group.
According to the above mathematical expressions, when only a value of Ri,0(k) is known, the indices of the row at which the k-th weight-1 is positioned in the i-th column group may be known. Therefore, when index values of the row at which the k-th weight-1 is positioned in the zero (0)-th column of each column group are stored, the positions of the column and the row at which the weight-1 is positioned may be understood in the parity-check matrix 300 (that is, the information word sub-matrix 310 of the parity-check matrix 300) having the structure illustrated in
According to the above-mentioned rules, all of the degrees of the columns belonging to the i-th column group are Di. According to the above-mentioned rules, the LDPC codes in which information on the parity-check matrix 300 is stored may be simply represented as follows.
As a specific example, when Nldpc is 30, Kldpc is 15, and Qldpc is three (3), position information of rows at which the weight-1 is positioned in zero (0)-th columns of three column groups may be represented by sequences as represented by following mathematical expression 4. The sequences represented by mathematical expression 4 may be called a weight-1 position sequence.
R1,0(1)=1,R1,0(2)=2,R1,0(3)=8,R1,0(4)=10,
R2,0(1)=0,R2,0(2)=9,R2,0(3)=13,
R3,0(1)=0,R3,0(2)=14, (4)
In mathematical expression 4 above, Ri,j(k) represents the indices of the row at which the k-th weight-1 is positioned in the j-th column of the i-th column group.
The weight-1 position sequences as represented by the above mathematical expression 4, which represents the indices of the rows at which one (1) is positioned in the zero (0)-th column of each column group, may be more simply represented like following Table 1.
Table 1 above shows the positions of entries having the weight-1, that is, value one (1) in the parity-check matrix, in which an i-th weight-1 position sequence is represented by the indices of the row at which the weight-1 is positioned in the zero (0)-th column belonging to the i-th column group.
When the column and the row of the parity-check matrix 300 illustrated in
Qldpc·i+j⇒M·j+i (0≤i<M,0≤j<Qldpc) (5)
i⇒i(0≤i<Kldpc)
Kldpc+Qldpc·k+l⇒Kldpc+M·l+k (0≤k<M,0≤l<Qldpc) (6)
In the above, the row permutation represents that an order of the rows of the parity-check matrix 300 is changed using mathematical expression 5 above. Further, the column permutation represents that an order of columns of the parity-check matrix 300 is changed using mathematical expression 6 above.
A method of performing permutation based on mathematical expressions 5 and 6 above is as follows. In this case, the column permutation is applied with the same principle as the row permutation, except the fact that the column permutation is applied only to the parity sub-matrix 320 by i⇒i (0≤i<Kldpc). Hereinafter, the row permutation will be described as an example.
In the case of the row permutation, i and j meeting X=Qldpc×i+j for an X-th row are calculated, and the calculated i and j are substituted in M×j+i to calculate a row in which the X-th row is permuted. For example, in the case of a seventh row, i and j meeting 7=2×i+j each are 3 and 1 and therefore the seventh row is permuted to a thirteenth (10×1+3=13) row.
When the row and column of the parity-check matrix of
Referring to
The parity-check matrix 400 illustrated in
Hereinafter, M×M matrices forming the parity-check matrix 400 having the form of
First, an M×M matrix 440 of an (Nqc_column−1)-th column-block among the zero (0)-th row-blocks has a form as represented by following mathematical expression 7.
In the M×M matrix as represented by mathematical expression 7 above, all the values of the zero (0)-th row and an M−1-th column are ‘0’. For 0≤i≤(M−2), an (i+1)-th row of the i-th column is ‘1’ and all the other values are ‘0’.
Second, in the parity sub-matrix 420 of the parity-check matrix 400 of
Third, the information word sub-matrix 410 may be a form in which a matrix Pa
The quasi-cyclic matrix P is represented by following mathematical expression 8.
The quasi-cyclic matrix P of the above mathematical expression 8 is a square matrix having an M×M size and is a matrix of which the respective degrees of M rows and columns forming the quasi-cyclic matrix P are one (1).
If a subscript aij of the quasi-cyclic matrix P is 0, the quasi-cyclic matrix P0 represents a unit matrix IM×M, and if the subscript aij of the quasi-cyclic matrix P is ∞, the quasi-cyclic matrix P∞ represents a zero matrix. As illustrated in
The parity-check matrix 400 as illustrated in
In the case of the LDPC codes, the codeword performance is determined according to the parity-check matrix. Specifically, the codeword performance may be determined according to a weight distribution and a cycle distribution of columns and rows.
The weight distribution of columns represents how many columns have one (1) and how many ones (1s) are positioned in the columns, in the Nldpc columns. Further, the weight distribution of rows represents how many rows have one (1) and how many ones (1s) are positioned in the rows, in the Nldpc−Kldpc rows. Further, a weight or a degree of one (1) represents the number of ones (1s) of each column and row.
Herein, the weight distribution of columns and rows may be determined based on a method called density evolution (reference: Richardson, T., and URBANKE, R.: ‘The capacity of low-density parity-check codes under message-passing decoding’, IEEE Trans. Inf. Theory, 2001, 47, (2), pp. 599-618).
In detail, in the case of using the density evolution method, when the LDPC encoding/decoding are performed based on the parity-check matrix having the given degree distribution, it may be estimated how many times of iteration is required for coding error probability to be ‘0’ at any signal to noise ratio (SNR). In the case of the density evolution, since it is estimated whether the coding error probability is ‘0’ under the assumption that the codeword length is infinite, the degree distribution of the parity-check matrix may not be determined only by the density evolution if the parity-check matrix for codes having a finite length is designed.
Further, the number of ones (1s) depending on the degree distribution of the parity-check matrix affects encoding/decoding complexity, and thus, the parity-check matrix needs to be designed based on the code performance which is verified not only based on a theoretical approach called the density evolution but also on the actual encoding/decoding complexity and the deigned parity-check matrix.
Hereinafter, a method for designing a parity-check matrix will be described in detail.
The form of a parity-check matrix may be very variously present, but the inventive concept intends to design a parity-check matrix having a specific form illustrated in
Hereinafter, the method for designing a parity-check matrix according to an exemplary embodiment will be described in detail.
Step 1) The sizes Nldpc and Kldpc and the values of M and Qldpc of the parity-check matrix to be designed are determined.
According to an exemplary embodiment, the foregoing parameters of the parity-check matrix may be determined as following Table 2.
In the case of the parity-check matrix 400 having the form of
Hereinafter, in step 2, the number of quasi-cyclic matrix, not the zero matrix, is determined.
Step 2) The degree distribution of the parity-check matrix is determined by the density evolution method.
As described above, the distribution of one (1) in the parity-check matrix dominates the performance of the LDPC codes. Therefore, according to an exemplary embodiment, the distribution of one (1) in the parity-check matrix is determined by the density evolution method. That is, a degree distribution having the highest probability for error probability to converge to a predetermined value by performing iterative decoding as many as a predetermined times, that is, a degree distribution having the lowest SNR is selected from all the possible degree distributions.
In this case, restrictions are as follows.
1) The number of ones (1s) in an LDPC code affects the encoding and decoding complexity, and thus, the number of ones (1s) needs to be limited.
2) If the number of ones (1s) present in a column is various, the decoding complexity may be increased, and thus, a kind of the number of ones (1s) needs to be limited.
First, all the possible degree distributions (lists) are determined based on the parity-check matrix having parameters of the above Table 2 in consideration of the foregoing restrictions. Next, after a target SNR for each code rate is determined, when the LDPC codes encoded/decoded based on the parity-check matrix having the degree distributions present in the list at the target SNR by the density evolution are decoded, it is determined how many time of iteration is required for the error probability to converge to a predetermined value.
In this case, for all the degree distributions present in the list, when the error probability is converged to a predetermined value or less within the number of iteration times smaller than a specific value, the target SNR value is adjusted to be small and the density evolution for the degree distribution is performed again.
However, when the result value of the density evolution for all the degree distribution is not converged even within more iterations than the specific value, the SNR value is adjusted to be large and the density evolution for the degree distribution is performed again.
Among all the degree distributions present in the list, the degree distribution in which the error probability is converged to the predetermined value or less within the low SNR and the small iterative decoding (that is, iteration number of times) is determined as the result of step 1.
Step 3) The position of the non-zero quasi-cyclic matrix is determined based on the degree distribution determined in step 2.
In this step, the position of the non-zero quasi-cyclic matrix is determined based on a well known PEG algorithm (X.-Y Hu, E. Eleftheriou, and D.-M. Arnold, “Regular and irregular progressive edge-growth tanner graphs”, IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 386-398, January 2005.) In this case, additional restrictions suggested by the present invention are to make the number of is in each row maximally uniform.
Step 4) The indices of the quasi-cycle matrices need to be adjusted so as to prevent the error floor from occurring.
In this step, the parity sub-matrix is fixed, and thus, is not considered. In the information word sub-matrix, only the index values of non-zero quasi-cycle matrices positioned in a predetermined row need to be changed from a column having the lowest column degree.
In this step, all index values of the non-zero quasi-cycle matrices, except the parity sub-matrix 420, positioned in the same row need to have different values.
The order of the rows at which the index values are changed may be various. A change in the index values is repeated until a cycle value of a minimum cycle is no more increased or the number of variable nodes having the minimum cycle is no more improved. Here, step 4 is called lifting.
Step 5) The parity-check matrix designed based on
In this case, the row permutation may be performed based on following mathematical expression 9 and the column permutation may be performed based on following mathematical expression 10.
M·i+j⇒Qldpcj+i (0≤i<Qldpc,0≤j<M) (9)
i⇒i(0≤i<Kldpc)
Kldpc+M·k+l⇒Kldpc+Qldpc·l+k (0≤k<Qldpc·0≤l<M) (10)
Hereinafter, a process of designing a parity-check matrix will be described in more detail with reference to a case of a code rate 10/15 (=2/3) as an example.
Step 1) Parameters Nldpc and Kldpc related to the size and the values of M and Qldpc of the parity-check matrix to be designed are determined as following Table 3.
Step 2) The degree distribution of the parity-check matrix is determined based on the density evolution method.
The distributions in which the error probability is highly likely to be a predetermined value at the lowest SNR as a result of the density evolution are selected from all the possible degree distributions. For example, for the selected distributions, when SNR=2.6 dB, the iteration number of times to make BER=10−5 is obtained by the density evolution method. The selected distributions and the iteration number of times obtained based on the density evolution for the selected distributions are as shown in following Table 4. In following Table 4, N (xi) represents the number of column groups or column blocks having a degree of xi.
Step 3) The positions of the non-zero quasi-cyclic matrix is determined based on the degree distribution determined in step 2.
According to an exemplary embodiment, a degree distribution of case 6 of above Table 4 is selected. Further, to meet the selected degree distribution, positions of the non-zero quasi-cycle matrix is determined.
The reason of determining case 6 is that, as described above, the number of ones (1s) depending on the degree distribution of the parity-check matrix affects encoding/decoding complexity, and thus, the parity-check matrix needs to be designed based on the code performance which is not only based on a theoretical approach called the density evolution but also on the actual encoding/decoding complexity and the deigned parity-check matrix.
Step 4) The indices of the quasi-cycle matrices need to be adjusted so as to prevent the error floor from occurring.
Following Table 5 shows positions and index values of the quasi-cycle matrices of the parity-check matrix 400 having the form of
Step 5) The parity-check matrix designed based on
Hereinafter, examples of the parity-check matrix designed by the foregoing method for designing a parity-check matrix will be described.
It is well known that any parity-check matrix H1 is equivalent to a parity-check matrix H2 obtained by performing row permutation and column permutation on the parity-check matrix H1. That is, any parity-check matrix having the form of
Further, a parity-check matrix having the form of
As a specific example, in the case in which Nldpc is 30, Kldpc is 15, and Qldpc is 3, if a case in which position information about rows at which weight-1s are positioned in zero (0)-th columns of three column groups is represented as following Table 6,
When y is 2,
since 1→(1+3×2)mod 15=7
2→(2+3×2)mod 15=8
8→(8+3×2)mod 15=14
10→(10+3×2)mod 15=1
0→(0+3×2)mod 15=6
9→(9+3×2)mod 15=0
13→(13+3×2)mod 15=4
0→(0+3×2)mod 15=6
14→(14+3×2)mod 15=5,
the parity-check matrices are equivalent to one another even when the position information about the row at which the weight-1s are positioned in the zero (0)-th columns of the three column groups is represented as following Table 7.
Further, the parity-check matrices are equivalent to one another even when an order of the column groups is changed, and thus, the parity-check matrices represented as the following Table 8 are also equivalent to one another.
Further, in the case of the parity-check matrix having the form of
Hereinafter, examples of a parity-check matrix having the form of
As an example, if a codeword length Nldpc is 64800, a code rate R is 6/15, M is 360 and Qldpc is 108, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
That is, positions of a row at which one (1) is positioned in a zero (0)-th column of each column group may be defined by indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group shown in above Table 9, and, by shifting a row at which one (1) is positioned in a zero (0)-th column of each column group by Qldpc, rows at which one (1) is positioned in other columns of the column group may be defined.
In the foregoing example, since Qldpc=(64800−25920)/360=108 and the indices of the row at which one (1) is positioned in the zero (0)-th column of the zero (0)-th column group are 891, 2309, 3615, . . . , the indices of the row at which one (1) is positioned in the 1-th column of the zero (0)-th column group may be 999 (=891+108), 2417 (=2309+108), 3723 (=3615+108), . . . and the indices of the row at which one (1) is positioned in the second column of the zero (0)-th column group may be 1107 (=999+108), 2525 (=2417+108), 3831 (=3723+108), . . . .
A parity-check matrix may also be defined by the method described in above Table 9, according to an exemplary embodiment.
As another example, if a codeword length Nldpc is 64800, the code rate R is 8/15 , M is 360 and Qldpc is 84, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example, if a codeword length Nldpc is 64800, the code rate R is 10/15, M is 360 and Qldpc is 60, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example, if a codeword length Nldpc is 64800, the code rate R is 12/15, M is 360 and Qldpc is 36, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
Meanwhile, in the design process of codes, the process of step 4 uses the lifting method considering the cycle characteristics. When various algebraic characteristics as well as the cycle characteristics are additionally considered, codes having better performance may also be designed.
Generally, since the performance of the LDPC codes affects the degree distribution as well as the cycle characteristics, codes having better performance may be designed in consideration of both of the two characteristics.
According to an exemplary embodiment, parameters may be determined depending on cycles having the shortest length and the number of variable nodes included in these cycles and having a specific degree, and a sequence may be determined depending on a rule determined based on the parameters in a lifting step.
For example, when the lifting process is applied to a column group of which the degrees are A and B, only a cycle in which the number of variable nodes of which the degree is A among the variable nodes included in the cycle while the lifting of the column group of which the degree is A is performed is x1 or less and a value of the variable nodes (the number of variable nodes of which the degree is A+the number of variable nodes of which the degree is B×C) included in the cycle while the lifting of the column group of which the degree is B is x2 or less may be considered.
However, all cycles are considered when the lifting process is applied to the column groups of which the degrees are not A and B.
Here, A is a positive integer of two (2) or more, B is a positive integer larger than A and smaller than a maximum degree of the parity-check matrix, and C is a weighting factor and has a positive integer value.
In addition, all cycles are considered without distinction of a specific cycle when the lifting process is applied to the column groups of which the degrees are not A and B.
As a specific example, the case in which A=3, B=4, and C=2 will be described.
For example, in the lifting process, the lifting is performed in consideration of only cycles in which the number of variable nodes (which is equivalent to columns) of which the degree is three (3) among the variable nodes included in the cycles in the process of performing the lifting of column groups of which the degrees are three (3) is x1 or less and (the number of variable nodes of which the degree is 4×2+the number of variable nodes of which the degree is three (3)) among variable nodes included in the cycles in the process of performing the lifting of column groups of which the degree is four (4) is x2 or less.
That is, when the index values are changed in the lifting process, the lifting process is repeated until the number of variable nodes having the cycles is not improved to change the index values depending on the degrees of each variable node in consideration of only the cycles corresponding to the conditions.
Generally, in simple lifting, a parity-check matrix is designed so that the number of cycles is decreased. In this process, the parity-check matrix is designed such that the number of cycles meeting the above-mentioned conditions is decreased.
The reason why the above-mentioned conditions affect the design of LDPC codes having better performance is that the cycles and the degree distributions affecting the LDPC codes have been considered in the above-mentioned conditions.
Examples of the LDPC codes designed in consideration of these additional conditions are shown in following Tables 13 to 18. For reference, the same length and code rate as those of the LDPC codes as shown in above Tables 9 to 12 are designed, values (x1, x2) considered in following Table 13 are equal to (4, 5), values (x1, x2) considered in following Table 14 is equal to (4, 5), (x1, x2) considered in following Table 15 are equal to (3, 4), and values (x1, x2) considered in following Table 16 are equal to (3, 4). Further, values (x1, x2) considered in following Table 17 are equal to (8, 8) and (x1, x2) considered in following Table 18 is equal to (3, 4).
As an example of results designed in consideration of these additional conditions, if a codeword length Nldpc is 64800, a code rate R is 6/15, M is 360, and Qldpc is 108, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example of results designed in consideration of these additional conditions, if codeword length Nldpc is 64800, a code rate R is 8/15, M is 360, and Qldpc is 84, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example of results designed in consideration of these additional conditions, if a codeword length Nldpc is 64800, a code rate R is 10/15, M is 360, and Qldpc is 60, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example of results designed in consideration of these additional conditions, if a codeword length Nldpc is 64800, a code rate R is 12/15, M is 360, and Qldpc is 36, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example of results designed in consideration of these additional conditions, if a codeword length Nldpc is 64800, a code rate R is 6/15, M is 360, and Qldpc is 108, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
As another example of results designed in consideration of these additional conditions, if a codeword length Nldpc is 64800, a code rate R is 10/15, M is 360, and Qldpc is 60, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group of a parity-check matrix having the structure of
Here, it is to be noted that even if the parity-check matrix in which an order of indices within a sequence for each i-th column group in any of above Tables 9 to 18 is changed, the changed parity-check matrix may also be applied to the same codes to which the original parity-check matrix applies.
For example, as shown in above Table 11, the sequence corresponding to the zero (0)-th column group is arranged in an order of 114, 2135, 3045, 4635, 5512, 5681, 6571, 8943, 10053, 10109, 13161, 13668, 14218, 17417, 19328, 21140, and even if the sequence has a changed index order like 2135, 8943, 4635, 114, 3045, 10109, 13161, 21140, 5681, 6571, 5512, 19328, 14218, 13668, 17417, 10053, a parity-check matrix having the changed sequence may be used for the same codes.
In addition, even if one index sequence of one column group is changed to an index sequence of another column group and vice versa, that is, an index sequence of the other column group is changed to the index sequence of the first column group, in above Tables 9 to 18, algebraic characteristics such as the cycle characteristics and the degree distributions on a graph of codes are not changed. Therefore, this case of changing index sequences between column groups of a parity-check matrix is another exemplary embodiment of the inventive concept.
For example, in above Table 11, the index sequence 114, 2135, 3045, 4635, 5512, 5681, 6571, 8943, 10053, 10109, 13161, 13668, 14218, 17417, 19328, 21140 of the zero (0)-th column group and the index sequence 19, 768, 1263, 3305, 6513, 7677, 7956, 9040, 13427, 16641, 17280, 18452, 18584, 18925, 19559, 20587 of a twelfth column group can be changed to set the sequence of the zero (0)-th column group to be 19, 768, 1263, 3305, 6513, 7677, 7956, 9040, 13427, 16641, 17280, 18452, 18584, 18925, 19559, 20587, and the sequence of the twelfth column group is set to be 114, 2135, 3045, 4635, 5512, 5681, 6571, 8943, 10053, 10109, 13161, 13668, 14218, 17417, 19328, 21140. That is, even if the index sequences are exchanged between the zero (0)-th column group and the twelfth column group, the cycle characteristics, the degree distributions, and the like in terms of the graph of codes are not changed (actually, since exchanging the index sequences between corresponding column groups is the same as changing only the arranging order of column groups within a parity-check matrix, the main algebraic characteristics are not changed).
In addition, a parity-check matrix in which an integer multiple of Qldpc is added to all indices of any column group in above Tables 9 to 18 may also result in the same algebraic characteristics such as the cycle characteristics and the degree distributions on the graph of the codes, according to an exemplary embodiment.
For example, if a multiple of 60 (that is, Qldpc=(Nldpc−Kldpc)/M=60) is added to all indices 12575, 15845 and 18200 of a twenty-fourth column group in above Table 11, that is, the indices are changed to 12635 (=12575+60), 15905 (=15845+60), and 18260 (=18200+60), the algebraic characteristics such as the cycle characteristics and the degree distributions on the graph of codes are not changed (actually, since a sequence obtained by adding an integer multiple of Qldpc in a column group has the same effect as rearranging only the order of columns within the column group, the main algebraic characteristics are not changed).
Here, it is to be noted that in the case in which an index value obtained by adding an integer multiple of Qldpc to a given index sequence is a value of Nldpc−Kldpc or more, the index value is changed and applied to a value obtained by performing a modulo operation on Nldpc−Kldpc.
For example, since a result of adding only 60×60 to the sequence 12575, 15845 and 18200 of the twenty-fourth column group in above Table 11 becomes 16175, 19445 and 21800 while Nldpc−Kldpc=21600, the changed sequence may be 16175, 19445 and 200 or 200, 16175 and 19445 by applying modulo-21600 to a result of adding only the integer multiple of Qldpc to the given sequence.
Hereinafter, a process of encoding LDPC codes using a parity-check matrix having the structure as illustrated in
Hereinafter, if it is assumed that LDPC encoded information word bits are (i0, i1, . . . , iK
First, since the LDPC code is a systematic code, ck for 0<k<Kldpc−1) is set to be the same as ik. In addition, the remaining codeword bits are set to be Pk:=ck+K
Meanwhile, according to an exemplary embodiment, since the parity-check matrix is defined by in above Tables 9 to 18, a process to be described below may be applied in the case in which the parity-check matrix is defined by in above Tables 9 to 18.
First, if it is assumed that an entry notated in a j-th position of an i-th row in above Tables 9 to 18 is q (i, j, 1)=q (i, j, 0)+Qldpc·1 (mod Nldpc−Kldpc) for 0<1<360. Here, accumulation ‘+’ means additions defined in a Galois field (GF) (2) (that is, additions in GF (2)). In addition, Qldpc, which is a size of each column cyclically shifted in an information word sub-matrix, may be a value defined in above Tables 9 to 18, respectively.
Meanwhile, when q (i, j, 0) and q (i, j, 1) are defined as described above, a process of calculating parity bits is as follows.
Step 1) The parity bits are initialized to ‘0’. That is, pk=0 for 0<k<Nldpc−Kldpc.
Step 2) i and l are set to be and i:=└k/360┘ and l:=k (mod 360) for all k values of 0<k<Kldpc. Here, └x┘ is the largest integer value among integers that are not larger than x. That is, └1.2┘=1. Next, ik is added to pq (i, j, 1) for all js as following based on the set i and l values. That is, pq (i, 0, 1)=pq (i, 0, 1)+ik, pq (i, 1, 1)=pq (i, 1, 1)+ik, pq (i, 2, 1)=pq (i, 2, 1)+ik, . . . , pq (i, w(i)−1, 1)=pq (i, w(i)−1, 1)+ik are calculated.
Here, w (i) is the number of values of the i-th row in above Tables 9 to 18 and represents the number of ones (1s) in a column corresponding to ik in the parity-check matrix. In addition, q (i, j, 0), which is the entry notated in the j-th position of the i-th row in above Tables 9 to 18, is an index of the parity bit and represents a position of a row at which one (1) is positioned in a column corresponding to ik in the parity-check matrix.
Step 3) Pk=Pk+pk−1 is calculated for all ks meeting 0<k<Nldpc−Kldpc to calculate the parity bits pk.
The parity bits are calculated by the foregoing method, such that all the LDPC codeword bits c0, c1, . . . , CN
Meanwhile, the LDPC encoding process as described above is only an example. That is, since the LDPC encoding process is a process of calculating an LDPC codeword C satisfying H·CT=0, various encoding methods for the given parity-check matrix may be present.
For example, a scheme applied in the DVB-T2 standard may also be applied to the case in which the parity-check matrix is defined by above Tables 9 to 18. Hereinafter, the LDPC encoding process according to the scheme described in the DVB-T2 standard will be schematically described using an example in which the parity-check matrix is defined in above Table 11.
First, if it is assumed that information word bits having a length of Kldpc are [i0, i1, i2, . . . , iK
Step 1) The parity bits are initialized to ‘0’. That is, p0=p1=p2= . . . =pN
Step 2) A zero (0)-th information word bit i0 is accumulated in a parity bit which has an address of a parity bit defined in a first row (that is, a row of i=0) of above Table 11 as the index of the parity bit. This may be represented by following mathematical expressions 11.
p114=p114⊕i0 p10053=p10053⊕i0
p2135=p2135⊕i0 p10109=p10109⊕i0
p3045=p3045⊕i0 p13161=p13161⊕i0
p4635=p4635⊕i0 p13668=p13668⊕i0
p5512=p5512⊕i0 p14218=p14218⊕i0
p5681=p5681⊕i0 p17417=p17417⊕i0
p6571=p6571⊕i0 p19328=p19328⊕i0
p8943=p8943⊕i0 p21140=p21140⊕i0 (11)
In the above mathematical expressions, i0 represents a zero (0)-th information word bit, pi represents an i-th parity bit, and ⊕ represents a binary operation. According to the binary operation, 1⊕1 is 0, 1⊕0 is 1, 0⊕1 is 1, and 0⊕0 is 0.
Step 3) The remaining 359 information word bits im (m=1, 2, . . . , 359) are accumulated in the parity bits. Here, the remaining information word bits may be information word bits which belong to the same column group as a column group to which i0 belongs. In this case, the addresses of the parity bits may be determined based on following mathematical expression 12.
(x+(m mod360)×Qldpc)mod(Nldpc−Kldpc) (12)
In above mathematical expression 12, x is an address of a parity bit accumulator corresponding to the information word bit i0, and Qldpc is 60 as a size of each column which is shifted in a sub-matrix corresponding to the information word.
As a result, each of the information word bits im (m=1, 2, . . . , 359) is accumulated in each parity bit having the addresses of the parity bits calculated based on above mathematical expression 12 as indices. As an example, operations as represented by following mathematical expression 13s may be performed on the information word bit i1.
p174=p174⊕i1 p10113=p10113⊕i1
p2195=p2195⊕i1 p10169=p10169⊕i1
p3105=p3105⊕i1 p13221=p13221⊕i1
p4695=p4695⊕i1 p13728=p13728⊕i1
p5572=p5572⊕i1 p14278=p14278⊕i1
p5741=p5741⊕i1 p17477=p17477⊕i1
p6631=p6631⊕i1 p19388=p19388⊕i1
p9003=p9003⊕i1 p21200=p21200⊕i1 (13)
In above mathematical expression, i1 represents a 1-th information word bit, pi represents an i-th parity bit, and ⊕ represents a binary operation. According to the binary operation, 1⊕1 is 0, 1⊕0 is 1, 0⊕1 is 1, and 0⊕0 is 0.
Step 4) A 360-th information word bit i360 is accumulated in a parity bit which has an address of a parity bit defined in a second row (that is, a row of i=1) of above Table 11 as the index of the parity bit.
Step 5) The remaining 359 information word bits belonging to the same group as a group to which the information word bit i360 belongs are accumulated in the parity bit. In this case, the address of the parity bit may be determined based on above mathematical expression 6. However, in this case, x is an address of a parity bit accumulator corresponding to the information word bit i360.
Step 6) the foregoing processes of Step 4 and Step 5 are repeated for all of the column groups of above Table 5.
Step 7) As a result, the parity bit pi is calculated based on following mathematical expression 14. Here, i is initialized to one (1).
pi=pi⊕pi−1i=1,2, . . . ,Nldpc−Kldpc−1 (14)
In above mathematical expression 14, pi represents an i-th parity bit, Nldpc represents the LDPC codeword length, Kldpc represents the information word length in the LDPC codeword, and ⊕ represents a binary operation. According to the binary operation, 1⊕1 is 0, 1⊕0 is 1, 0⊕1 is 1, and 0⊕0 is 0.
According to the above method, the parity bits may be calculated.
Meanwhile, the addresses of the parity bit present in the zero (0)-th column of the i-th column group are the same as the indices of the row at which one (1) is positioned in the zero (0)-th column of the i-th column group. Therefore, the indices of the row at which one (1) is positioned in the zero (0)-th column of the i-th column group in above Tables 9 to 18 are represented as addresses of the parity bits in the encoding process. Therefore, above Tables 9 to 18 may show “addresses of parity bit accumulators”.
As described above, according to the above exemplary embodiments, the LDPC encoding process may be performed using various schemes to generate an LDPC codeword.
Meanwhile, LDPC codes may be decoded using an iterative decoding algorithm based on the sum-product algorithm on the bipartite graph illustrated in
Hereinafter, a message passing operation generally used for LDPC decoding will be described with reference to
In this case, a message update rule based on the sum-product algorithm may be represented by following mathematical expressions 15.
In above mathematical expressions 15, Sign (En, m) indicates a sign of the message En, m, and En, m indicates a magnitude of the message En, m. Meanwhile, a function Φ(x) may be represented by following mathematical expression 16.
Ty,x=Ex+Σy′∈M(x)/yEy′,x (17)
In above mathematical expression 17, Ex represents an initial message value of the variable node x.
In addition, when a bit value of the node x is decided, it may be represented by following mathematical expression 18.
Px=Ex+Σy′∈M(x)Ey′,x (18)
In this case, an encoding bit corresponding to the node x may be decided depending on a value of Px.
In
As illustrated in
Here, the parity-check matrix may have the same structure as that of the parity-check matrix 300 illustrated in
In detail, the parity-check matrix includes the information word sub-matrix and the parity sub-matrix described above.
Here, the information word sub-matrix is formed of a plurality of column groups each including M columns and may be defined by a table indicating positions of value one (1) present in every M-th column. Here, M, which is an interval at which patterns of columns are repeated in the information word sub-matrix, may be 360. In addition, the parity sub-matrix may have a dual diagonal structure.
In this case, the LDPC encoder 610 may perform the LDPC encoding using parity-check matrices differently defined depending on a code rate (that is, a code rate of the LDPC codes).
For example, the LDPC encoder 610 may perform the LDPC encoding using parity-check matrices defined by a table such as above Tables 9, 13 and 17 when the code rate is 6/15, and perform the LDPC encoding using parity-check matrices defined by a table such as above Tables 10 and 14 when the code rate is 8/15. Further, the LDPC encoder 610 may perform the LDPC encoding using parity-check matrices defined by a table such as above Tables 11, 15 and 18 when the code rate is 10/15, and perform the LDPC encoding using parity-check matrices defined by a table such as above Tables 12 and 16 when the code rate is 12/15.
Meanwhile, a detailed method for performing the LDPC encoding is already described, and thus, duplicate descriptions thereof will be omitted.
The encoding apparatus 600 may further include a memory (not illustrated) in which information on a code rate, a codeword length and a parity-check matrix of an LDPC code is previously stored, and the LDPC encoder 610 may perform LDPC encoding using this information. Here, the information on the parity-check matrix may comprise information about an information word sub-matrix which is formed of a plurality of column groups each including M columns and a table showing positions of value one (1) present in every M-th column.
The BCH encoder 710 performs BCH encoding on input bits and outputs a BCH codeword generated by BCH encoding to the LDPC encoder 720.
In detail, the BCH encoder 710 performs the BCH encoding on the input bits L=[l0, l1, . . . , lK
The BCH encoding is a well-known technology and is disclosed in “Bose, R. C.; Ray-Chaudhuri, D. K. (March 1960), “On A Class of Error Correcting Binary Group Codes”, Information and Control 3 (1): 68-79, ISSN 0890-5401”, etc., and thus, detailed descriptions thereof will be omitted herein.
Meanwhile, it may be changed whether the BCH encoder 710 is used. That is, in some cases, the BCH encoder 710 may also be omitted.
The LDPC encoder 720 performs LDPC encoding on the BCH codeword output from the BCH encoder 710 and outputs an LDPC codeword generated by the LDPC encoding to the interleaver 730.
In detail, the LDPC encoder 720 performs the LDPC encoding on the BCH codeword Ildpc=[i0, i1, i2, . . . , iK
However, when the BCH encoder 710 is omitted, the LDPC encoder 720 may perform the LDPC encoding on the input bits.
Meanwhile, the LDPC encoder 720 of
To this end, the transmitting apparatus 700 may include a memory (not illustrated) for storing the information on the parity-check matrix. In this case, the parity-check matrix may be various depending on the code rate and may be the table defined by above Tables 9 to 18 as an example. Here, the information on the parity-check matrix may comprise the information regarding information word sub-matrix which is formed of the plurality of column groups each including M columns and a table showing positions of value one (1) present in every M-th column.
The interleaver 730 performs interleaving on the LDPC codeword output from the LDPC encoder 720 and outputs the interleaved bits to the modulator 740.
In this case, the interleaver 730 receives an LDPC codeword bit string output from the LDPC encoder 720 to perform the interleaving using a predetermined scheme. The interleaving scheme may be variously present and it may be variable whether or not the interleaver 730 is used.
The modulator 740 modulates the bit string output from the interleaver 730 and transmits the modulated bit string to a receiving apparatus (for example, 1000 of
In detail, the modulator 740 may demultiplex bits output from the interleaver 730 and map the demultiplexed bits to constellation.
That is, the modulator 740 may convert the bits output from the interleaver 730 in a serial-to-parallel scheme to generate cells formed of a predetermined number of bits. Here, the number of bits forming each cell may be equal to the number of bits forming modulation symbols which are mapped to the constellation.
Next, the modulator 740 may map the demultiplexed bits to the constellation. That is, the modulator 740 modulates the demultiplexed bits using various modulation schemes such as QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM to generate the modulation symbols, and map the generated modulation symbols to constellation points. In this case, the demultiplexed bits are formed of the cells corresponding to the modulation symbols, and thus, each cell may sequentially be mapped to the constellation points.
Further, the modulator 740 may modulate signals mapped to the constellation and transmit the modulated signals to the receiving apparatus 1000. For example, the modulator 740 may map the signals, which are mapped to the constellation, to an OFDM frame by using an orthogonal frequency division multiplexing (OFDM) scheme and transmit the mapped signals to the receiving apparatus 1000 through an allocated channel.
The transmitting apparatus 700 may pre-store various parameters which are used for encoding, interleaving, and modulation. Here, the parameters used for encoding may be information on the code rate and the codeword length of the BCH codes and the information on the code rate, the codeword length, and the parity-check matrix of the LDPC codes. Further, the parameters used for interleaving may be information on an interleaving rule and the parameter used for modulation may be information on the modulation schemes. Here, the information on the parity-check matrix may comprise the information regarding information word sub-matrix which is formed of the plurality of column groups each including M columns and a table showing positions of value one (1) present in every M-th column.
In this case, each component configuring the transmitting apparatus 700 may be operated using the parameters.
Meanwhile, although not illustrated, the transmitting apparatus 700 may further include a controller (not illustrated) for controlling an operation of the transmitting apparatus 700.
In this case, the controller (not illustrated) may provide the information on the code rate and the codeword length of the BCH codes to the BCH encoder 710 and provide the information on the code rate, the codeword length, the parity-check matrix of the LDPC codes to the LDPC encoder 720. Further, the controller (not illustrated) may provide the information on the interleaving schemes to the interleaver 730 and the information on the modulation schemes to the modulator 740. Here, the information on the parity-check matrix may comprise the information regarding information word sub-matrix which is formed of the plurality of column groups each including M columns and a table showing positions of value one (1) present in every M-th column.
The LDPC decoder 810 performs LDPC decoding on an LDPC codeword based on a parity-check matrix. Here, the LDPC codeword may be formed of 64800 bits. That is, the LDPC codeword length may be 64800.
For example, the LDPC decoder 810 passes log likelihood ratio (LLR) values corresponding to the LDPC codeword bits using an iterative decoding algorithm to perform the LDPC decoding, thereby generating information word bits.
Here, the LLR values may be represented by channel values corresponding to the LDPC codeword bits by various methods.
For example, the LLR values may be represented by values obtained by taking a log on a ratio of a probability that bits transmitted through the channel at the transmitting side are zero (0) and a probability that bits are one (1). Further, the LLR values may be bit values determined by a soft decision and may also be a representative value determined depending on a section to which the probability that the bits transmitted from the transmitting side are zero (0) or one (1) belongs.
In this case, the transmitting side may use the LDPC encoder 610 as illustrated in
Meanwhile, the parity-check matrix used for the LDPC decoding may have the same form as that of the parity-check matrix 300 illustrated in
In detail, the parity-check matrix includes the information word sub-matrix and the parity sub-matrix.
Here, the information word sub-matrix is formed of a plurality of column groups each including M columns and is defined by the table indicating positions of value one (1) present in every M-th column. Here, M, which is an interval at which patterns of columns are repeated in the information word sub-matrix, may be 360. In addition, the parity sub-matrix may have a dual diagonal structure.
In this case, the LDPC decoder 810 may perform the LDPC decoding using the parity-check matrices differently defined depending on a code rate (that is, a code rate of LDPC codes).
For example, the LDPC decoder 810 may perform the LDPC decoding using parity-check matrices defined by a table such as above Tables 9, 13 and 17 when the code rate is 6/15, and perform the LDPC decoding using parity-check matrices defined by a table such as above Tables 10 and 14 when the code rate is 8/15. Further, the LDPC decoder 810 may perform the LDPC decoding using parity-check matrices defined by a table such as above Tables 11, 15 and 18 when the code rate is 10/15 and perform the LDPC decoding using parity-check matrices defined by a table such as above Tables 12 and 16 when the code rate is 12/15.
As described above, the LDPC decoder 810 may perform the LDPC decoding using an iterative decoding algorithm. In this case, the LDPC decoder 810 may be configured as illustrated in
As illustrated in
The input processor 911 stores an input value. In detail, the input processor 911 may store the LLR values of signals received through a wireless channel.
The controller 914 determines the number of values input to the variable node operator 913, an address value in the memory 912, the number of values input to the check node operator 915, an address value in the memory 912, and the like, based on a size (that is, a codeword length) of a block of the signal received through the wireless channel and a parity-check matrix corresponding to the code rate.
According to the exemplary embodiment, indices of a row at which one (1) is positioned in a zero (0)-th column of an i-th column group may perform the decoding based on the parity-check matrices defined by above Tables 9 to 18.
The memory 912 stores the input data and output data of the variable node operator 913 and the check node operator 915.
The variable node operator 913 receives data from the memory 912 based on information on the address of the input data and information on the number of input data which are received from the controller 914 to perform a variable node operation. Next, the variable node operator 913 stores variable node operation results in the memory 912 based on information on the address of the output data and information on the number of output data which are received from the controller 914. Further, the variable node operator 913 inputs the variable node operation results to the output processor 916 based on data which are received from the input processor 911 and the memory 912. Here, the variable node operation is already described with reference to
The check node operator 915 receives data from the memory 912 based on the information on the address of the input data and the information on the number of input data which are received from the controller 914 to perform a variable node operation. Next, the check node operator 915 stores variable node operation results in the memory 912 based on information on the address of the output data and information on the number of output data which are received from the controller 914. Here, the check node operation is already described with reference to
The output processor 916 performs a soft decision on whether information word bits of the codeword at the transmitting side are zero (0) or one (1) based on data received from the variable node operator 913 and then outputs soft-decision results, such that an output value of the output processor 916 may be a value which is finally decoded. In this case, in
The decoding apparatus 800 may further include a memory (not illustrated) in which information on the code rate, the codeword length, and the parity-check matrix of the LDPC code is previously stored, and the LDPC decoder 810 may perform the LDPC encoding using this information. However, this is only an example, and thus, corresponding information may be provided from the transmitting side. Here, the information on the parity-check matrix may comprise information about an information word sub-matrix which is formed of a plurality of column groups each including M columns and a table showing positions of value one (a) present in every M-th column.
The demodulator 1010 receives and demodulates a signal transmitted from the transmitting apparatus (for example, 700 of
In this case, the value corresponding to the LDPC codeword may be represented by a channel value for the received signal. Here, a method for determining the channel value may be various and may be a method for determining an LLR value as one example.
The deinterleaver 1020 may perform deinterleaving on output values of the demodulator 1010 and output deinterleaved output values to the LDPC decoder 1030.
In detail, the deinterleaver 1020 is a component corresponding to the interleaver 730 of the transmitting apparatus 700 and may perform an operation corresponding to the interleaver 730. That is, the deinterleaver 1020 may inversely apply the interleaving scheme applied to the interleaver 730 to deinterleave LLR values output from the demodulator 1010.
However, in some cases, when the interleaver 730 is omitted in the transmitting apparatus 700, the deinterleaver 1020 may be omitted.
The LDPC decoder 1030 may use output values of the deinterleaver 1020 to perform the LDPC decoding and output LDPC decoded bits to the BCH decoder 1040. Here, the LDPC decoded bits may be a BCH codeword.
In detail, the LDPC decoder 1030 is a component corresponding to the LDPC encoder 720 of the transmitting apparatus 700, and may perform the LDPC decoding based on a parity-check matrix. The LDPC decoder 1030 of
The BCH decoder 1040 may perform the BCH decoding on values output from the LDPC decoder 1030.
In detail, the BCH decoder 1040 is a component corresponding to the BCH encoder 710 of the transmitting apparatus 700 and may perform the BCH decoding on a BCH codeword output from the LDPC decoder 1030 to generate the bits transmitted from the transmitting apparatus 700. However, in some cases, when the BCH encoder 710 is omitted in the transmitting apparatus 700, the BCH decoder 1040 may be omitted.
The receiving apparatus 1000 may pre-store various parameters which are used for decoding and interleaving. Here, the parameters used for decoding may be information on a code rate and a codeword length of the BCH code and information on a code rate, a codeword length and a parity-check matrix of the LDPC code. Further, the parameters used for deinterleaving may be information on a deinterleaving rule. Here, the information on the parity-check matrix may comprise information about an information word sub-matrix which is formed of a plurality of column groups each including M columns and a table showing positions of value one (1) present in every M-th column.
In this case, each component configuring the receiving apparatus 1000 may be operated using the parameters.
Meanwhile, although not illustrated, in some cases, the receiving apparatus 1000 may further include a controller (not illustrated) for controlling an operation of the receiving apparatus 1000.
In this case, the controller (not illustrated) may provide the information on the code rate and the codeword length of the BCH codes to the BCH decoder 1040 and provide the information on the code rate, the codeword length, the parity-check matrix of the LDPC codes to the LDPC decoder 1030. Further, the controller (not illustrated) may also provide the information on the interleaving scheme to the deinterleaver 1020. Here, the information on the parity-check matrix may comprise the information regarding information word sub-matrix which is formed of the plurality of column groups each including M columns and a table showing positions of value one (a) present in every M-th column.
As described above, when the LDPC encoding is performed based on the parity-check matrix defined according to the above exemplary embodiments, it may be appreciated that the BER/FER performance is improved.
First, the LDPC encoding is performed on input bits based on a parity-check matrix to generate an LDPC codeword (S1310). In this case, the LDPC codeword may be formed of 64800 bits. That is, the LDPC codeword length may be 64800.
Meanwhile, the parity-check matrix may have the same form as that of the parity-check matrix 300 illustrated in
In detail, the parity-check matrix includes the information word sub-matrix and the parity sub-matrix described above.
Here, the information word sub-matrix is formed of a plurality of column groups each including M columns and may be defined by a table indicating positions of value one (1) present in every M-th column. Here, M, which is an interval at which patterns of columns are repeated in the information word sub-matrix, may be 360. In addition, the parity sub-matrix may have a dual diagonal structure.
In this case, in S1310, the LDPC encoding may be performed using parity-check matrices which are differently defined depending on a code rate.
For example, the LDPC encoding may be performed using parity-check matrices defined by a table such as above Tables 9, 13 and 17 when the code rate is 6/15 and the LDPC encoding may be performed using parity-check matrices defined by a table such as above Tables 10 and 14 when the code rate is 8/15. Further, the LDPC encoding may be performed using parity-check matrices defined by a table such as above Tables 11, 15 and 18 when the code rate is 10/15 and the LDPC encoding may be performed using parity-check matrices defined by a table such as above Tables 12 and 16 when the code rate is 12/15.
Meanwhile, a detailed method for performing the LDPC encoding is already described, and thus, duplicate descriptions thereof will be omitted.
First, the LDPC decoding is performed on an LDPC codeword based on a parity-check matrix (S1410). Here, the LDPC codeword may be formed of 64800 bits. That is, the LDPC codeword length may be 64800.
For example, the LDPC decoding may be performed by passing LLR values corresponding to the LDPC codeword bits through an iterative decoding algorithm to generate information word bits.
Here, the LLR values may be represented by channel values corresponding to the LDPC codeword bits by various methods.
For example, the LLR values may be represented by values obtained by taking a log on a ratio of a probability that bits transmitted through a channel at the transmitting side are zero (0) and a probability that bits are one (1). Further, the LLR values may be bit values determined by a soft decision and may also be a representative value determined depending on a section to which the probability that the bits transmitted from the transmitting side are zero (0) or one (1) belongs.
In this case, the transmitting side may use the LDPC encoder 610 as illustrated in
Meanwhile, the parity-check matrix may have the same form as that of the parity-check matrix 300 illustrated in
In detail, the parity-check matrix includes the information word sub-matrix and the parity sub-matrix as described above.
Here, the information word sub-matrix is formed of a plurality of column groups each including M columns and may be defined by a table indicating positions of value one (1) present in every M-th column. Here, M, which is an interval at which patterns of columns are repeated in the information word sub-matrix, may be 360. In addition, the parity sub-matrix may have a dual diagonal structure.
In this case, in S1410, the LDPC decoding may be performed using parity-check matrices which are differently defined depending on a code rate R.
For example, the LDPC decoding may be performed using parity-check matrices defined by a table such as above Tables 9, 13 and 17 when the code rate is 6/15 and the LDPC decoding may be performed using parity-check matrices defined by a table such as above Tables 10 and 14 when the code rate is 8/15. Further, the LDPC decoding may be performed using parity-check matrices defined by a table such as above Tables 11, 15 and 18 when the code rate is 10/15 and the LDPC decoding may be performed using parity-check matrices defined by a table such as above Tables 12 and 16 when the code rate is 12/15.
Meanwhile, the detailed method for performing the LDPC decoding is already described, and thus, duplicate descriptions thereof will be omitted.
A non-transitory computer readable medium in which programs sequentially performing the encoding method and the decoding method according to the above exemplary embodiments are stored may be provided.
The non-transitory computer readable medium is not a medium such as a register, a cache, and a memory which may store data for a short period of time but a medium which may semi-permanently store data and read by equipment. In detail, various applications or programs as described above may be stored and provided in the non-transitory computer readable medium such as a compact disc (CD), a digital versatile disc (DVD), a hard disk, a Blu-ray disk, a universal serial bus (USB), a memory card, and a read-only memory (ROM).
Further, in the foregoing block diagram illustrating the encoding apparatus, the decoding apparatus, the transmitting apparatus, and the receiving apparatus, a bus is not illustrated, but communication between each component in the encoding apparatus, the decoding apparatus, the transmitting apparatus, and the receiving apparatus may be made through the bus.
Components, elements or units represented by a block as illustrated in
As described above, according to the exemplary embodiments, the LDPC encoding and decoding performance may be improved.
Hereinabove, although various exemplary embodiments of the inventive concept are illustrated and described, the inventive concept is not limited to the aforementioned exemplary embodiment and it is apparent that various modifications can be made to those skilled in the art without departing from the spirit of the inventive concept described in the appended claims and the modified embodiments are not to be individually understood from the technical spirit and prospects of the inventive concept.
| Number | Date | Country | Kind |
|---|---|---|---|
| 10-2014-0058599 | May 2014 | KR | national |
This application is a continuation of U.S. application Ser. No. 16/523,369 filed Jul. 26, 2019, which is a continuation of U.S. application Ser. No. 14/303,834 filed Jun. 13, 2014 which is now U.S. Pat. No. 10,411,736 issued Sep. 10, 2019, which claims priority from Korean Patent Application Nos. 10-2014-0058599, filed on May 15, 2014, in the Korean Intellectual Property Office, and U.S. Provisional Application Nos. 61/862,208, 61/841,502, and 61/835,096, filed on Aug. 5, 2013, Jul. 1, 2013, and Jun. 14, 2013, respectively, in the United States Patent and Trademark Office, the disclosures of which are incorporated herein by reference in their entirety.
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| Child | 16523369 | US |
