Patent Application
20080091986
In order to address the above-mentioned need for contention-free interleavers, a method and apparatus for selecting interleaver sizes for turbo codes is provided herein.
During operation an information block of size K is received. An interleaver size K′ is determined where K′ is related to K″ where K″ is from a set of sizes; wherein the set of sizes comprise K″=ap×f, pmin≦p≦pmax; fmin≦f≦fmax, wherein a is an integer, f is a continuous integer between fmin and fmax, and p takes integer values between pmin and pmax, a>1, pmax>pmin, pmin>1. The information block of size K is padded into an input block of size K′. The input block is interleaved using an interleaver of size K′. The original input block and the interleaved input block are encoded to obtain a codeword block. The codeword block is transmitted trough the channel.
In a further embodiment of the present invention the step of determining the interleaver size K′ that is related to K″ comprise the step of using K′=K″.
In yet another embodiment of the present invention the step of determining the interleaver size K′ that is related to K″ comprise the step of using K′=K″ when K″ is not a multiple of (2m−1); otherwise using K′=K″+δ(K″) when K″ is a multiple of (2m−1), wherein m is the memory length of the constituent convolutional encoder, and δ(K″) is a small positive or negative integer not equal to a multiple of (2m−1). In one embodiment m=3.
In yet another embodiment of the present invention the step of interleaving the input block comprises the step of using a permutation π(i)=(i P0+A+d(i))mod K′, where 0≦i≦K′−1 is the sequential index of the symbol positions after interleaving, π(i) is the symbol index before interleaving corresponding to position i, K′ is the interleaver size in symbols, P0 is a number that is relatively prime to K′, A is a constant, C is a small number that divides K′, and d(i) is a dither vector of the form d(i)=α(i mod C)+P0×β(i mod C) where α(·) and β(·) are vectors each of length C, periodically applied for 0≦i≦K′−1.
Prior to describing encoding and decoding data, the following definitions are provided to set the necessary background:
Turning now to the drawings, wherein like numerals designate like components,
During operation of transmitter 100, information block of size K needs to be encoded by the turbo encoder 101. For some communication systems where a large number of different Ks are used, it is not efficient (and often impossible) to define a contention-free (CF) interleaver for every information block size K. It is preferable if a small set (K′) of well-designed CF interleavers is able to cover all the information block sizes. Given an information block size K, a suitable interleaver size K′ may be chosen by circuitry 103 from the set of available sizes (e.g., interleaver sizes listed in table 105). The information block is then padded into an input block of size K′ by circuitry 109 and sent as input to the turbo encoder 101. A typical arrangement is to pad the information block with Kfiller filler bits (via filler insertion circuitry 109). Note that the term “size” and “length” are used interchangeably to indicate the number of elements in a block or vector.
Once K′ is chosen by circuitry 103, it is provided to turbo encoder 101. During encoding, a contention-free interleaver may be used (not shown in
The output of turbo encoder 101 comprises a codeword block x, and x is sent to transmitter 107 where it is transmitted through the channel. The transmitter may perform additional processing such as rate matching, channel interleaving, modulation, etc., before transmitting the codeword block x through the channel.
Interleaver 201 can be a contention-free interleaver. An interleaver π(i), 0≦i<K′, is said to be contention-free for a window size W if and only if it satisfies the following constraint for both ψ=π (interleaver) and ψ=π−1 (de-interleaver),
where 0≦j<W, 0≦t; ν<M(=K′/W), and t≠ν. Though it is not always necessary, for efficient turbo decoder design, typically all the M windows are full, where K′=MW. The terms in (1) are the memory ban addresses that are concurrently accessed by the M processors when writing the extrinsic values to the output memory bans during iterative decoding. If these memory bank addresses are all unique during each read and write operations, there are no contentions in memory access and hence the (de)interleaving latency can be avoided, leading to a high speed decoder implementation.
During operation of turbo encoder 101, input block of length K′ bits enters both interleaver 201 and encoding circuitry 202. Interleaver 201 can be a contention-free interleaver of size K′.
Interleaver 201 interleaves the input block and passes the input block in interleaved order to encoding circuitry 203. Encoding circuitry 203 then encodes the interleaved input block. In a similar manner, encoding circuitry 202 encodes the original input block. The codeword block x is composed of systematic block (equal to the input block), output of encoding circuitry 202, and output of encoding circuitry 203. The codeword block x is then sent to transmitter 107 which can also receive a copy of the input block directly.
As an example of the contention-free interleaver, an almost regular permutation (ARP) interleaver is given by the following expression
π(i)=(iP0+A+d(i))mod K′
where 0≦i≦K′−1 is the sequential index of the bit positions after interleaving, π(i) is the bit index before interleaving corresponding to position i, K′ is the interleaver size, P0 is a number that is relatively prime to K′, A is a constant, C is a small number that divides K′, and d(i) is a dither vector of the form d(i)=α(i mod C)+P0×β(i mod C) where α(·) and β(·) are vectors each of length C, periodically applied for 0≦i≦K′−1. Both α(·) and β (·) are composed of multiples of C. The overall interleaver π(·) thus constructed has quasi-cyclic (i.e., periodic) properties with period C, and when Used in tail-biting turbo codes, the turbo code itself becomes quasi-cyclic leading to a simplified code design procedure.
If interleaver 201 can satisfy (1) for various values of M, then the decoder can be implemented using various degrees of parallelism (one for each M). Thus it is desirable to choose K′ that has various factors. For an A interleaver of length K′, any window size W where W is a multiple of C and a factor of K′, can be used for high-speed decoding without memory access contentions. This provides flexibility and scalability in decoder design by allowing a wide range of parallelism factors M. Thus, a good compromise between decoding speed and complexity can be made based on system (or classes of user elements) requirements.
As discussed above, interleaver size determination circuitry 103 needs to determine an interleaver size K′ for a given K, This section describes a way of selecting a limited number of sizes (i.e., K′) for which turbo code interleavers may be defined. As indicated previously, filler insertion circuitry (along with puncturing or rate-matching methods) may be used to handle any information block size K. In general, the interleaver size selection must take into consideration the decoding burden and performance degradation due to the filler bits.
The number of filler bits Kfiller padded to an information block to form an input block is desirable to be limited to a small percent (e.g., around 10-13%) of the information block size K. This is achieved by limiting the difference between adjacent interleaver sizes, i.e., adjacent K′ values (assuming all available K′ values are sorted in ascending order). The number of filler bits are minimized by choosing the smallest K′ available such that K′≧K. The number of filler bits is Kfiller=K′−K. However, other available values of K′≧K may also be chosen, if desired.
Consider the following set of sizes defined to cover information sizes between Kmin and Kmax.
K″=a
p
×f, p
min
≦p≦p
max
; f
min
≦f≦f
max, (2)
where a is an integer, f is a continuous integer between fmin and fmax, and p takes integer values between pmin and pmax, a>1, pmax>pmin, pmin>1. Although not necessary, one can choose these parameters such that Kmin=apmin×fmin, and Kmax=apmax×fmax, while discarding any sizes that may not be needed. This method of selecting a limited set of sizes to cover a rage of information block sizes is referred to as semi-log slicing. For a given information block of size K, a size K′ related to a K″ based on the semilog-slicing table, and input block size K.
The semilog slicing is similar to the companding operation employed in compressing signals of large dynamic range, for example, A-law and mu-Law companders used in speech codecs. The semilog slicing rule allows an efficient design to cover a wide-range of information block sizes.
Of the several ways of choosing the parameters, one way of choosing fmin and fmax values is to let K″ values resulting from adjacent p line up with each other, i.e., ap×(fmax+1)=ap+1×fmin, thus
ti fmax=a×fmin−1
For a given value of p, the separation between two adjacent block sizes K″ is given by ap, which means that a maximum of ap−1 filler bits are added if the information block size K is in group p and the interleaver size is equal to K″. Thus, the fraction of filler bits Kfiller over the information block size K is bounded as shown below, which occurs when the block size K is slightly greater than the size given by (p, fmin), and using K′=K″ given by p,fmin+1) to,
Alternatively, K″ values resulting from adjacent p can line up with each other via ap×fmax=ap+1x(fmin−1), resulting in fmax=a×(fmin−1). This would give a similar Kfiller/K bound. Therefore, the parameters for the semi-log slicing can be tuned according to the range of block sizes to be supported, and also on the tolerable fraction of filler bits. The choice of fmin requires a balance between the following two requirements:
The semi-log slicing method is very simple in that for any block size, the interleaver size K′ to be used may be easily determined based on a K″ computed from (2). Once the semilog slice sizes are defined (K″), the interleaver size K′ may be obtained from the semilog slice sizes (without deviating subtantially) by, for example,
For example, if a=2, fmin=8, and fmax=15, then interleaver sizes of the form K′=K″=2p×14 are multiples of 7, and hence are invalid interleaver sizes when using tail-biting 3GPP TC. Therefore, this case must be handled with slight alteration, e.g., using K′=K″ when K″ is not a multiple of 7; otherwise using K′=K″+δ(K″) when K″ is a multiple of 7, and δ(K″) is a small positive or negative integer not equal to a multiple of 7.
For the K″ sizes that are invalid choice for ARP interleavers, one simple way to determine a related interleaver size K′ is by subtracting (addition is just as valid) d×C from K″, where d(is a small positive integer and d(is not a multiple of 7, and C is a AC interleaver cycle length used for the block sizes next to K′ in the set of available sizes. (Recall that the block size of an ARP interleaver is a multiple of the cycle lengths C.) In other words,
K′=K″−dC (3)
or
K′=K″+dC (4)
when K″ is a multiple of 7. Since C is normally an even integer, such as, 4, 8, 12, or 16, this adjustment gives two advantages, namely, (a) K′ is not a multiple of 7, and (b) K′ is a multiple of C and hence an ARP interleaver for size K′ can be designed.
For simplicity, the same d can be chosen for all K″ that need to be adjusted. One important consideration for choosing d is that it should be such that all sizes obtained by (3) or (4) have a substantial number of factors, which allows supporting a wide range of parallelism for the CF interleaver thus defined.
A set of CF ARP interleavers suitable to cover information block sizes for 3GPP Long Term Evolution (LTE) is shown in Table 1. The interleaver sizes available in table 105 are defined based on the semi-log slicing method described above. Specifically,
K″=2p×f, p=4,5, . . . , 9; f=8,9, . . . , 15, (5)
and K′ is determined from K″. The interleaver sizes are determined as follows: using K′=K″ and for p=4,5,6,7,8,9 and f=8,9,10,11,12,13,15, and using K′=K″−dC for p=4,5,6,7,8,9 and f=14, covering K from 128 to 7680. The last thee sizes (f=13, 14, 15) corresponding to p=9 may be removed such that Kmax=6144, with Kmin=128. Equation (3) is used along with d=2 when f=14 (i.e., to avoid interleaver sizes that are multiples of 7) in order to handle tail-biting TC. These sizes are highlighted in Table 1. Once the interleaver sizes in 105 are determined, a CF interleaver may be designed for each interleaver size.
Given any information block size K, the circuitry 103 can determine the interleaver size K′ to be used for K by choosing the smallest value of K′ from 105 that is greater than or equal to K. With K known, and fmin=2b, fmax=2b+1−1, where b is an integer, the parameters p and f can be calculated as follows,
p=└log2(K)┘−3 (8)
With the parameters p and f the block size K′ can be calculated using (2) or (5), and moreover, when f is a multiple of 7 and tail-biting encoding is used, interleaver size calculated using (3) or (4) may be used in addition. The parameters associated with the interleaver of size K′ is then looked up from the storage means for interleaver parameter 105, which is normally stored in memory for the communication device.
Storage means for interleaver parameter 105 may store ARP interleaver parameters using the values of K′, C, P0, α(·) and β (·) that are taken from at least one row of Table 1. The interleaver 201 may use an ARP interleaver with the values of K′, C, P0, α(·) and β (·) that are taken from at least one row of the following table:
There are several ways to modify the interleaver table. For example, storage can be reduced by using a set of ARP parameters that apply to more than one interleaver size. For example, the 1024-bit, 2048-bit, 4096-bit interleavers can all use the same ARP parameters. In another variation, some of the rows of the table may be redesigned based on different C values, if needed. I n another enhancement, some of the entries of the parameters (e.g., α(0) and β(0)) may be fixed (e.g., always zero).
Following are some further comments on the interleaver selection procedure used to obtain Table 1.
As discussed above, in one embodiment K′=K″. In yet another embodiment K″=K″ when K″ is not a multiple of (2m−1), otherwise using K′=K″+δ(K″) when K″ is a multiple of (2m−1), wherein m is the memory length of a constituent convolutional encoder, and δ(K″) is a small positive or negative integer not equal to a multiple of (2m−1) In one embodiment, m=3.
Interleaver 402 utilizes permutation π(i)=(iP0+A+d(i))mod K′, where 0≦i≦K′−1 is the sequential index of the symbol positions after interleaving, π(i) is the symbol index before interleaving corresponding to position i, K′ is the interleaver size in symbols, P0 is a number that is relatively prime to K′, A is a constant, C is a small number that divides K′ and 4(i) is a dither vector of the form d(i)=α(i mod C)+P0×β(i mod C) where α(·) and β(·) are vectors each of length C, periodically applied for 0≦i≦K′−1. The values of K′, C, P0, α(·) and β (·) are preferably taken from a row of Table 1. The deinterleaver 401 performs an inverse function of interleaver 402.
At step 503 filler insertion circuitry 109 receives an information block of size K and pads the information block of size K into an input block u of size K′ and outputs the input block u. Interleaver 201 then interleaves he input block of size K′ (step 507) (preferably using a contention-free interleaver) and sends the interleaved block of size K′ to encoding circuitry 203 (step 509). Finally, at step 511, the original input block and interleaved input block are encoded.
As discussed above, the step of interleaving the input block comprises the step of using a permutation π(i)=(iP0+A+d(i))mod K′, where 0≦i≦K′−1 is the sequential index of the bit positions after interleaving π(i) is the bit index before interleaving corresponding to position i, K′ is the interleaver size in bits, P0 is a number that is relatively prime to K′, A is a constant, C is a small number that divides K′, and d(i) is a dither vector of the form d(i)=α(i mod C)+P0×>β(i mod C) where α(·) and β(·) are vectors each of length C, periodically applied for 0≦i≦K′−1. The values of K′, C, P0, α(·) and β (·) are preferably taken from Table 1.
While the invention has been particularly shown and described with reference to a particular embodiment, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. In one example, the interleaver table may be enhanced further to handle special cases, including: (a) Using an additional set of interleaver sizes defined to cover any special block sizes that must be handled, e.g., without filler bits or with fewer filler bits. (b) The interleaver sizes can be slightly adjusted by adding or subtracting a small value from the semilog slice sizes. In another example, although the invention has been described above assuming binary-input turbo encoder, the same principle can be applied when the turbo encoder takes symbols as input. For example, a duo-binary turbo code takes a symbol of two binary bits at a time, and the turbo interleaver permutes symbols (further scrambling such as alternating the bits within a symbol may be performed). In such a case, the input block size is measured in symbols, and the interleaver size is equal to the number of symbols in the input block. In another example, although the above description assumes that the interleaver sizes and the interleaver parameters are stored in a look-up table, it is possible that they may be determined via other means such as algebraic calculation. In yet another example, although the above description assumes a turbo code, the method is also applicable to other FEC schemes including, for example low-density parity-check (LDPC) codes, Reed-Solomon (RS) Codes, etc. it is intended that such changes come within the scope of the following claims.
