CN108833052B

CN108833052B - Channel polarization decoding path metric value sorting method

Info

Publication number: CN108833052B
Application number: CN201810388527.4A
Authority: CN
Inventors: 甘明; 李晓光; 周世阳; 兰天
Original assignee: Southwest Electronic Technology Institute No 10 Institute of Cetc
Current assignee: Southwest Electronic Technology Institute No 10 Institute of Cetc
Priority date: 2018-04-26
Filing date: 2018-04-26
Publication date: 2021-02-26
Anticipated expiration: 2038-04-26
Also published as: CN108833052A

Abstract

The invention discloses a path metric value ordering method for channel polarization decoding. The invention can greatly reduce processing and storage devices and obviously reduce decoding time delay. The invention is realized by the following technical scheme: when the decoding of the SCL is expanded to the ith layer, L candidate paths of the ith-1 layer are input, each path corresponds to a group of sequences and serves as a father path of the expansion of the ith layer, and on the L father paths, each path is expanded according to the addition bits 0 and 1 to obtain 2L sub candidate paths; then, the decoder divides the path metric values of the 2L sub-paths into odd sequences and even sequences according to the sequence numbers, wherein the odd sequences are ascending sequences, and the even sequences are unordered sequences. Sequencing the even sequences from small to large according to a parity sequencing network method, and outputting the sequences; and merging the odd sequence with the length of L and the sequence with the length of L by using a parity merger to obtain the ascending sequence with the length of 2L.

Description

Channel polarization decoding path metric value sorting method

Technical Field

The present invention relates to a (channel Polar code) Polar code SCL decoding path competition method in the field of coding and decoding in a wireless communication system, and more particularly, to a decoding method and a decoder of Polar codes.

Background

Since the channel has different degrees of noise interference in actual communication, the received information may have different degrees of errors, thereby reducing the reliability of the communication system. Therefore, designers of digital communication systems are concerned with a core problem of how to reproduce information in a channel with noise interference as reliably as possible so as to reduce errors in information transmission, and at the same time, to achieve both effectiveness and reliability of the communication system without reducing transmission efficiency of the information system. The channel polarization is a processing process of transforming an original channel, changing the channel capacity and differentiating into two poles. Channel polarization was originally found on B-DMC channels, but the phenomenon of channel polarization is ubiquitous, and channel polarization can be performed on other channels, provided that the channels must be symmetric.The channel polarization depends on the type of channel used, with different channels having different channel polarization methods. The BEC channel has the simplest polarization method, the polarization of the BSC channel is complex, and the polarization information is difficult to obtain by a general method. The decoding of the polarization code is closely related to the performance of the polarization code, and the performance of the polarization code is greatly different due to different decoding algorithms. In 2008, Arikan first proposed the concept of channel polarization at the international Information Theory ISIT conference, and described in more detail in a paper published in 2009 in the journal of IEEE transmission on Information Theory, and at the same time, provided a coding scheme based on channel polarization, named Polar code. Polar codes are Channel Polarization (Channel Polarization) codes, and have become one of the research hotspots in the field of Channel coding today due to their low decoding complexity. Polar code in combination with other different codes has been applied to many technologies such as deep space communication, magnetic recording channels, and optical transmission systems. The polarization code is based on channel polarization, and a channel with good channel condition is selected to transmit information after the channel polarization, so that the performance of the polarization code is greatly improved, but the polarization code also has some inherent defects, which affects the practical application of the polarization code. The channel polarization is channel-specific, i.e., for different channels, there is a different channel polarization, which needs to be analyzed according to the specific channel situation. If the parameters of the channel are time-varying, the polarization code also varies from time to time, complicating the system. In addition to the simpler calculation of the channel polarization in BEC channels, the calculation of the channel polarization is usually more complex for other types of channels. For some more complex channels, it is not possible to calculate various parameters of the polar channels, limiting the use of polar codes on these channels. In addition, polar codes are generally used when the channel conditions are known, and if the channel conditions are unknown, they can be approximated by using a predicted channel, and when the approximation degree is poor, the polar code performance becomes poor. Since the SC decoding of the polar code is performed sequentially, only the previous symbol can be decoded, and only the next symbol can be decoded. This results in a large delay of the polar code when the code length is long, i.e. the throughput is affectedAnd (6) sounding. In the polarization code, before information is sent into a channel, the channel can function, a generating matrix is closely related to the channel, the channel can participate in the calculation of the generating matrix, and different generating matrices can be generated for different channels, and different code words can be formed; when decoding, the channel will also affect the decoding by some parameters. This is the difference between the polar code and the general channel coding, in short, the coding and decoding of the polar code are channel dependent. This is because the polarization of the channel is the basis of the polarization code, and the polarization of the channel depends on the channel type and the parameters of the channel itself, ultimately resulting in the channel-dependent nature of the polarization code. 2.1 channel polarization code is a low complexity construction code that achieves the channel capacity of a binary discrete memoryless channel (B-DMC) when SC decoding is used. The polarization of the channel is the basis of this coding method, and is a phenomenon: for N independent B-DMC channels, after input bits are subjected to a series of linear transformations, the input channels are transmitted, and except a small part of channels, the rest channels show the phenomenon that the channel capacity I (W) tends to 0 or 1. Although channel polarization is proposed based on binary discrete memoryless channels, the channel polarization phenomenon is ubiquitous, and other channels also have the channel polarization phenomenon. The channel polarization Polar code has a deterministic construction method, and is the first, and only known channel coding method which can be strictly proved to "reach" the channel capacity. Polar code is one of the alternative error correcting code schemes for 5G ultra-high speed transmission, however, Polar code still has some bottlenecks in practical ultra-high speed transmission application. Two major challenges faced by current Polar codes are the improvement of decoding throughput and short and medium code decoding performance. When Polar is proposed, Successive Cancellation (SC) decoding is adopted, the decoding complexity is low, but the decoding belongs to serial decoding, the delay is large, Belief Propagation (BP) decoding is a parallel decoding method, the Polar code decoding throughput can be improved, but the performance of the Polar code decoding is not obviously improved compared with SC decoding, and the decoding calculation complexity is high. In the prior art, based on the original SC Decoding, a SC Decoding (SCL) algorithm with a List is introducedAnd the decoding performance of the polarization code is greatly improved. For the traditional SC decoder, when decoding information bits, hard decision is directly made according to the corresponding log-likelihood ratio, and decoding is continued by using the decision result. However, the SCL decoding algorithm retains the most probable L decoding paths during the decoding process. When decoding information bits, the decoding path is branched downwards to 0 or 1, so as to obtain 2L alternative paths, and then L paths with higher probability are selected from the alternative paths. When decoding a fixed bit, the decision is directly made as the known bit 0. And after the decoding judgment of N bits is completed, selecting a decoding sequence corresponding to the path with the highest probability from the finally reserved L paths to obtain the decoding output of the SCL decoder. Because the SCL decoder does not immediately make hard decisions but keeps a plurality of possible values, the possibility of errors caused by the hard decisions can be reduced, and the final decoding performance is improved. The decoding performance of the SCL decoder is related to the search bandwidth L, the larger L, the better the performance. One key algorithm of the SCL decoder is path competition, i.e. the metric values of 2L candidate paths are sorted, and the L paths with the smallest path metric values are selected. The SCL algorithm can also be combined with CRC (CRC-assisted SCL, CA-SCL) decoding algorithm, the information source sequence contains CRC check information, and in the L candidate path sequences after SCL decoding, through selecting the candidate sequences capable of passing CRC check, the error correction capability of the decoding algorithm is improved, and the performance equivalent to or even better than that of other existing coding modes (Turbo and LDPC) is obtained. The delay stage of the sequencing processing will affect the decoding delay of the SCL, and the complexity of the logic for realizing the sequencing processing will affect the clock period of the maximum processing, and finally affect the throughput rate of the Polar code. Most of traditional sorting processing algorithms (counting, inserting, selecting, exchanging and the like) are serial processing, and for a serial sorting problem with n numbers, the lower bound of the delay is D-omega (nlog)₂n), that is to say that its latency cannot be less than a constant multiple nlog₂n is the same as the formula (I). When L is larger, the serial sequencing has more delay stages, and the throughput of the poralr code is limited.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides the path metric sorting method which can reduce the delay stage number of sorting processing, improve the decoding throughput of Polar codes and decode the SCL of the Polar codes.

The purpose of the invention can be realized by the following technical scheme: a path metric sorting method for channel polarization decoding is characterized by comprising the following steps:

when the decoding of the polarization code SCL is expanded to the ith layer, L candidate paths of the ith-1 layer are input, and each path corresponds to a group of sequences

u_k(k is more than or equal to 1 and less than or equal to i-1) is a decoding bit of the kth layer and is used as a father path of path expansion of the ith layer, and on L father paths, each path is subjected to path expansion according to the addition bits 0 and 1 to obtain 2L son candidate paths; the decoder then sets the path metric o to [ o ] for the 2L subpaths₁,o₂,...o_2L]，O_k(k is more than or equal to 1 and less than or equal to 2L) is the path metric value of the kth sub-path, and the path metric value sequence is divided into odd sequences [ o ] according to the sequence number₁,o₃,...,o_2L-1]And even sequence [ o ]₂,o₄,...,o_2L]The decoding characteristic is SC by the polar code of the channel, the odd sequence is ascending sequence, and the even sequence is unordered sequence. Will couple the sequence [ o ]₂,o₄,...,o_2L]Sorting from small to large according to the odd-even sorting network method, and outputting a sequence e ═ e₁,e₂,...,e_L]，e_k(1. ltoreq. k. ltoreq.L) is the kth element of the ascending sequence e; and then the odd sequence [ o ] with the length of L₁,o₃,...,o_2L-1]And a sequence of length L e ═ e₁,e₂,...,e_L]Merging by using an odd-even merger to obtain a ascending sequence [ p ] with the length of 2L₁,p₂,...,p_2L]，p_k(1. ltoreq. k.ltoreq.2L) is the kth element of the ascending sequence; reserving L candidate paths with smaller path metric values, and satisfying p₁≤p₂≤...≤p_LCandidate path metric value p₁,p₂,...p_L]As candidate paths and paths for the i-th layerMetric value

p_k ⁽ⁱ⁾And (k is more than or equal to 1 and less than or equal to 2L) is the path metric value of the kth candidate path of the ith layer.

Compared with the prior art, the invention has the following beneficial effects.

When SCL decoding is expanded to the ith layer, the invention inputs L candidate paths of the ith-1 layer, and each path corresponds to a group of sequences

As a father path of the ith layer path expansion, on the L father paths, each path is expanded according to the addition bits 0 and 1 to obtain 2L child candidate paths; the strategy of non-serial sequencing can obtain L optimal path metrics by comparing the path metric values in parallel, can reduce the delay progression of sequencing processing, and can reliably transmit information in a channel with noise interference. The decoding complexity is relatively low, the error correction performance is more excellent, and the requirement of a 5G mobile communication control channel on the error correction performance can be met.

The invention sets the path metric value o of 2L sub-paths at the decoding end as [ o ]₁,o₂,...o_2L]Divided into odd sequences [ o ] by sequence number₁,o₃,...,o_2L-1]And even sequence [ o ]₂,o₄,...,o_2L]The even sequence [ o ]₂,o₄,...,o_2L]Sorting from small to large according to the odd-even sorting network method, and outputting a sequence e ═ e₁,e₂,...,e_L](ii) a Then the odd sequence [ o ]₁,o₃,...,o_2L-1]And the sequence e ═ e₁,e₂,...,e_L]Merging is performed with a parity merger. And selecting the information bit sequence corresponding to the path with the highest probability as a decoding result, and if the L alternative paths do not meet CRC check, directly outputting the information bit sequence corresponding to the path with the highest probability value as the decoding result. The strategy of non-serial sequencing can obtain L paths by parallel comparison of the path metric valuesThe optimal path metric can reduce the delay progression of the sorting process, and the experimental result shows that the method can provide about 4 times of acceleration when the path selection module is equal to 16. The low complexity soft output decoding algorithm obtains better performance and greatly reduces processing and storage equipment, thereby not only reducing the use of hardware resources, but also reducing the decoding time delay and having the capability of meeting the requirements of a fifth generation mobile communication control channel on error correction performance and throughput rate.

Drawings

Fig. 1 is a basic flow chart of the path metric sorting method for channel polarization decoding according to the present invention.

FIG. 2 is a schematic diagram of an example path search of Polar code SCL decoding algorithm.

FIG. 3 is a graphical representation of a two input comparator.

Fig. 4 is an example of a (2, 2) parity merger.

Fig. 5 is an example of a (4,4) parity merger.

Fig. 6 is an example of an even sequence with L-4 ordered by a parity ordering network.

Fig. 7 is an example of an even sequence with L-8 ordered by a parity ordering network.

Fig. 8 is an example of merging and optimization of an odd sequence and an e sequence of L-4 using a parity merger.

Fig. 9 is an example of an ordering of the path metric values for L-4.

Detailed Description

See fig. 1. According to the invention, the following steps are carried out:

step 201, inputting L candidate paths and metric values p of the i-1 layer when calculating the I layer of SCL decoding_i-1And L is a natural number.

When SCL decoding is extended to the ith layer, L candidate paths of the ith-1 layer are input, and each path corresponds to a group of sequences

As the parent path of the i-th path extension, the path metric value is

And p is_i-1To ascending sequence, satisfy

The ith candidate path metric value of the (i-1) th layer is represented.

Step 202, on the L candidate paths, path expansion is performed on each path according to the added bits 0 and 1, and 2L sub-candidate paths are obtained through expansion.

For a parent path

Adding bits 0 and 1, respectively, expands into two new paths (u)₁,u₂,...,u_i-10) and (u)₁,u₂,...,u_i-1And 1), then L father paths are expanded into 2L son paths. Path metric value o corresponding to 2L sub-paths is ═ o₁,o₂,...o_2L]According to the recursive formula of Polar code path metric value, the calculation formula is as follows,

in the formula, L_lThe likelihood probability of the ith layer bit is calculated on the basis of the ith father path sequence, wherein L is more than or equal to 1 and less than or equal to L.

From the formulae (1) and (2), and

the path metric value o corresponding to 2L sub-paths satisfies the following two properties:

o_2l-1≤o_2(l+1)-1 (3)

o_2l-1≤o_2l (4)

wherein L is more than or equal to 1 and less than or equal to L.

FIG. 2 shows a path search example of Polar code SCL decoding algorithm.

The code length of the channel polarization code Polar is N, and the Polar codes all correspond to a full binary tree with the depth of N. Each layer of edge of the full binary tree corresponds to an information bit or a fixed bit respectively, edges between each node and the left and right successor nodes of the full binary tree are marked as 0 and 1 respectively except leaf nodes, and a decoder starts from a root node to a path with the length of N of any leaf node and corresponds to a decoding sequence with the fixed bit. The path formed by the decoder from the root node to any one of the nodes corresponds to a path metric value. The decoder expands the paths from the root node, and when each layer expands to the next layer, when the candidate paths are less than or equal to L, all the candidate paths are reserved; and when the candidate path is larger than L, carrying out sequencing pruning, and selecting L pieces with smaller path metric values in the current layer, wherein L is called the search width. And after arriving at the leaf node layer, outputting the decoding sequences corresponding to the L paths as a decoding candidate sequence set according to the sequence of the metric values from small to large.

In fig. 2, the code length N of polar code is 4, u₁Is a fixed bit, takes the value 0,

for an information bit, the value is (0,1,0), and the channel polarization code algorithm searches for a width L of 2.

101, the decoder performs the extension of the layer 1 edge by taking the root node as a search starting point, and the two candidate paths 0 and 1 are both reserved because the path number is equal to 2, and the path metric values are 0.13 and + ∞.

102, when the decoder expands at layer 2, 2 candidate paths are expanded into 4 new paths, respectively (0,0), (0,1), (1,0) and (1,1), with path metric values of 0.13, 0.61, + ∞and + ∞. Since the candidate path is greater than 2, two (0,0) and (0,1) with smaller path metric values, 0.13, 0.61, remain from the four candidate paths.

103, in layer 3 expansion, 2 candidate paths are expanded into 4 new paths, respectively (0,0,0), (0,0,1), (0,1,0), and (0,1,1), with path metric values of 0.92, 0.13, 1.35, and 0.61. Since the candidate path is greater than 2, two (0,0,1) and (0,1,1) with smaller path metric values are retained from the four candidate paths, whose path metric values are 0.13, 0.61.

104, in layer 4 expansion, 2 candidate paths are expanded into 4 new paths, respectively (0,0,1,0), (0,0,1,1) (0,1,1,0) and (0,1,1,1), with path metric values of 0.13, 0.86, 1.48 and 0.61. Since the candidate path is greater than 2, two (0,0,1,0) and (0,1,1,1) with smaller path metric values are retained from the four candidate paths, whose path metric values are 0.13, 0.61. Finally, the SCL decoding algorithm outputs (0,0,1,0) and (0,1,1,1) as the set of decoding candidate sequences.

In the SCL coding process, starting from the root node to the nth (n ═ log)₂L), the number of the candidate paths is less than or equal to the search width L, and sequencing pruning is not needed. Starting at the n +1 th layer, the expanded candidate paths are 2L, sorting pruning is needed, and L candidate paths are reserved. The sorting algorithm of the present invention is therefore directed to the n +1 th later layer computation of SCL decoding.

Step 203, dividing the path metric values of the sub-candidate paths into an odd sequence and an even sequence according to the sequence numbers.

Path metric value o for 2L subpaths ═ o₁,o₂,...o_2L]Divided into odd sequences [ o ] by sequence number₁,o₃,...,o_2L-1]And even sequence [ o ]₂,o₄,...,o_2L]. From equation (1), the odd sequence [ o ]₁,o₃,...,o_2L-1]Is that

To ascending sequence, satisfy

So the odd sequence [ o₁,o₃,...,o_2L-1]Satisfy o₁≤o₃≤...≤o_2L-1I.e., ascending sequence.

Step 204, the even sequence is sorted from small to large according to the method of the odd-even sorting network.

Pair sequence [ o ]₂,o₄,...,o_2L]And ordering from small to large according to a method of the odd-even ordering network, wherein the odd-even ordering network is constructed by adopting an odd-even merger.

Parity merger was proposed by Batcher in the end of the 60 s and was defined as follows:

is provided with two ascending sequences [ x ] to be merged₁,x₂,...,x_p]And [ y₁,y₂,...,y_q]A (p, q) parity merger, p ≧ q, can be recursively constructed as follows: if pq is equal to 1, the parity merger is a comparator shown in fig. 3; if pq > 1, merge the two odd sequences

And

obtaining an ordered sequence

Wherein

Represents rounding up; at the same time, merge the two even sequences

And

obtaining an ordered sequence

Wherein

Indicating a rounding down. Finally, the combined following sequence elements [ v₁,w₁,v₂,w₂,...,v_q,w_q,...,v_p]Two-by-two input comparator w₁:v₂w₂:v₃...w_q:v_q+1To obtain the final ascending sequence [ z ]₁,z₂,...,z_p+q]。

Referring to FIG. 4, in a (2, 2) parity merger, two ascending sequences [ x ] to be merged₁,x₂]And [ y₁,y₂]And p is 2. Because pq is 4>1, merging two odd sequences [ x ]₁]And [ y₁]Due to [ x ]₁]And [ y₁]And pq is 1 × 1 is 1, and is merged by using a comparator to obtain an ordered sequence [ v [₁,v₂](ii) a Merging two even sequences [ x ]₂]And [ y₂]Due to [ x ]₂]And [ y₂]And pq is 1 × 1 is 1, and is merged by using a comparator to obtain an ordered sequence [ w₁,w₂](ii) a Finally, the merged sequences are aligned [ v ]₁,w₁,v₂,w₂]W of₁:v₂Inputting the input into a comparator to obtain a final ascending sequence [ z ]₁,z₂,z₃,z₄]。

See fig. 5. FIG. A is a drawing. In a (4,4) parity merger, two ascending sequences [ x ] to be merged₁,x₂,x₃,x₄]And [ y₁,y₂,y₃,y₄]And p is 4. Because pq is 16>1, merging two odd sequences [ x ]₁,x₃]And [ y₁,y₃]Merging by using a (2, 2) odd-even merger to obtain an ordered sequence [ v₁,v₂,v₃,v₄](ii) a Merging two even sequences [ x ]₂,x₄]And [ y₂,y₄]Merging by using a (2, 2) odd-even merger to obtain an ordered sequence [ w₁,w₂,w₃,w₄](ii) a Finally, the merged sequences are aligned [ v ]₁,w₁,v₂,w₂,v₃,w₃,v₄,w₄]W of₁:v₂w₂:v₃w₃:v₄Input comparatorTo obtain the final ascending sequence [ z ]₁,z₂,z₃,z₄,z₅,z₆,z₇,z₈]. The comparator structure of fig. 5(a) is drawn as fig. 5(b), which are equivalent. A parity ordering network of even sequences is constructed using a plurality of parity combiners.

Said step 204 is an even sequence [ o ]₂,o₄,...,o_2L]Split into L ascending sequences: [ o ]₂]，[o₄]…[o_2L]The number of elements in each sequence is 1. L/2 (1,1) merger pairs are adopted to pair L/2 pairs of ascending sequences [ o₂]And [ o₄]，[o₆]And [ o₈]，…，[o_2L-2]And [ o_2L]Respectively merging to obtain L/2 ascending sequences with the length of 2; combining two sets of L/2 ascending sequences with the length of 2 into L/4 pairs of ascending sequences, merging the L/4 ascending sequences by adopting L/4 (2, 2) mergers respectively to obtain L/4 ascending sequences with the length of 4 … …, merging the 2 ascending sequences with the length of L/2 by adopting 1 (L/2 ) merger to obtain ascending sequences with the length of L, wherein the ascending sequences with the length of L are e [ [ e ] ]₁,e₂,...,e_L]。

Number of delay stages D of step 204₁：

Referring to fig. 6, in the case where an even sequence of L-4 is ordered by the parity ordering network, the even sequence [ o [ ] is₂,o₄,...,o₈]Split into 4 ascending sequences: [ o ]₂]，[o₄]，[o₆]，[o₈]The number of elements in each sequence is 1. 2 pairs of ascending sequences [ o ] using 2 (1,1) mergers₂]And [ o₄]，[o₆]And [ o₈]Respectively merging to obtain 2 ascending sequences with the length of 2, then merging the 2 ascending sequences with the length of 2 by using 1 (2, 2) merger to obtain ascending sequences with the length of 4, i.e. [ e ]₁,e₂,e₃,e₄]。

See fig. 7. An even sequence of L-8,ordering by parity ordering network, and ordering even sequence [ o ]₂,o₄,...,o₁₆]Split into 8 ascending sequences: [ o ]₂]，[o₄]…[o₁₆]The number of elements in each sequence is 1.

4 pairs of ascending sequences [ o ] were combined using 4 (1,1) mergers₂]And [ o₄]，[o₆]And [ o₈]，[o₁₀]And [ o₁₂]，[o₁₄]And [ o₁₆]Respectively merging to obtain 4 ascending sequences with the length of 2; combining two sets of 4 ascending sequences with the length of 2 into 2 pairs of ascending sequences, and then merging by adopting 2 (2, 2) mergers respectively to obtain 2 ascending sequences with the length of 4; merging 2 ascending sequences with the length of 4 by using 1 (4,4) merger to obtain an ascending sequence with the length of 8, i.e. [ e ]₁,e₂,...,e₈]。

Step 205, the odd sequence and the ascending sequence e output from step 204 are set to [ e ═ e₁,e₂,...,e_L]Merging with odd-even merger to merge ascending sequence o₁,o₃,...,o_2L-1]And the sequence e ═ e₁,e₂,...,e_L]Merging by using a (L, L) merger to obtain a ascending sequence [ p ] with the length of 2L₁,p₂,...,p_2L](ii) a From equation (3), in ascending sequence [ o ]₁,o₃,...,o_2L-1]The first element of (1) o_2l-1Then L-L +1 elements (including element m) are present in the sequence_2l-1) Has a value of o or more_2l-1From equation (4), the L-L +1 elements will be less than or equal to the even sequence [ o ]₂,o₄,...,o_2L]Corresponding L-L +1 elements, i.e. the even sequence [ o ]₂,o₄,...,o_2L]In which at least L-L +1 elements have a value greater than or equal to o_2l-1. Sequence e ═ e₁,e₂,...,e_L]Is an even sequence [ o ]₂,o₄,...,o_2L]Ordered ascending sequence, so the sequence e ═ e₁,e₂,...,e_L]At least L-L +1 elements having a value greater than or equal to o_2l-1I.e. by

o_2l-1≤e_l (5)

Optionally, the parity merger in step 205 may be further simplified.

The first stage of the parity merger in step 205 completes o_2l-1And e_l1,2, L. From equation (5), the stage comparator can be eliminated. For the merged 2L path metric values, the SCL decoder only retains the first L path metric values, and the sequence of the last L path metric values is irrelevant to the SCL decoding, so that a comparator only related to the sequence of the last L path metric values can be omitted.

Optionally, the parity merger in step 205 may be further simplified.

All comparators in the (L, L) parity merger that do not affect the first L orders are removed.

The number of delay stages D of step 205₂：

D₂＝log₂L

Fig. 8(a) is an odd sequence [ o ] of L-4₁,o₃,o₅,o₇]And e ═ e₁,e₂,e₃,e₄]An example of merging using a parity merger, and fig. 8(b) is an optimized example thereof.

FIG. 8(a) the ascending sequence [ o ]₁,o₃,o₅,o₇]And the sequence e ═ e₁,e₂,e₃,e₄]Merging by using a (4,4) odd-even merger to obtain a ascending sequence [ p ] with the length of 8₁,p₂,...,p₈]；

Fig. 8(b) removes the first stage comparators and (4,4) removes the first 4 sequential comparators of the parity merger.

Step 206, the L candidate paths and path metric values of the ith layer are retained.

The L candidate paths with smaller path metric values in the step 205 are retained, and the candidate path metric value [ p ]₁,p₂,...p_L]Satisfy p₁≤p₂≤...≤p_LAs candidate path and path metric value of the ith layer

Satisfy the requirement of

The sequencing delay of the method of the invention is in

steps

204 and 205, so the total sequencing delay D of the method of the invention:

comparison table for serial sequencing time delay

Searching for wideband L	2	4	8	16	32	64	128
								The invention	2	8	24	64	160	384	896
Serial sequencing	2	5	9	14	20	27	35

The total sorting delay and the lower bound (minimum) of the serial algorithm delay are compared according to the comparison table of the serial sorting delay, the serial algorithm delay is rapidly increased along with the increase of the search broadband L, and the delay advantage of the method is more obvious.

The sorting process according to the embodiment of the present invention is described in more detail below with reference to specific examples.

See fig. 9. In the path metric value ordering for the case where L is 4,

the first step, using 4 candidate paths of the i-1 th layer as father paths and path metric values

And secondly, carrying out sub-path expansion on each father path according to the addition bits 0 and 1 to obtain 8 sub-candidate paths. The path metric value is calculated according to the formulas (1) and (2), and 8 sub candidate path metric values o are obtained₁,o₂,o₃,o₄,o₅,o₆,o₇,o₈]。

Third, the path metric o is ═ o₁,o₂,o₃,o₄,o₅,o₆,o₇,o₈]Divided into odd sequences [ o ] by sequence number₁,o₃,o₅,o₇]Even sequence [ o ]₂,o₄,o₆,o₈]. Wherein the oddSequence [ o ]₁,o₃,o₅,o₇]Is that

Satisfy o₁≤o₃≤o₅≤o₇。

Fourth step, even sequence [ o ]₂,o₄,o₆,o₈]Sorting according to odd-even sorting network, and outputting ascending sequence e ═ e₁,e₂,e₃,e₄]。

Fifth step, the odd sequence [ o ]₁,o₃,o₅,o₇]And the ascending sequence e ═ e₁,e₂,e₃,e₄]Merging is performed using a (4,4) merger, where the first stage comparator of the parity merger is removed, and all comparators that do not affect the first 4 orders are removed.

Sixthly, keeping 4 candidate paths with smaller path metric value and candidate path metric value [ p ]₁,p₂,p₃,p₄]Satisfy p₁≤p₂≤p₃≤p₄As candidate path and path metric value of the ith layer

Satisfy the requirement of

And the total sequencing delay D is 5 when L is 4.

The foregoing detailed description of the embodiments of the present invention has been presented for purposes of illustration and description, and is intended to be exemplary only; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims

1. A path metric sorting method for channel polarization decoding is characterized by comprising the following steps:

u_k(k is more than or equal to 1 and less than or equal to i-1) is a decoding bit of the kth layer and is used as a father path of path expansion of the ith layer, and on L father paths, each path is subjected to path expansion according to the addition bits 0 and 1 to obtain 2L son candidate paths; the decoder then sets the path metric o to [ o ] for the 2L subpaths₁,o₂,...o_2L]，O_k(k is more than or equal to 1 and less than or equal to 2L) is the path metric value of the kth sub-path, and the path metric value sequence is divided into odd sequences [ o ] according to the sequence number₁,o₃,...,o_2L-1]And even sequence [ o ]₂,o₄,...,o_2L]The decoding characteristic of the channel polar code SC is that the odd sequence is a ascending sequence and the even sequence is a disordered sequence; will couple the sequence [ o ]₂,o₄,...,o_2L]Sorting from small to large according to the odd-even sorting network method, and outputting a sequence e ═ e₁,e₂,...,e_L]，e_k(1. ltoreq. k. ltoreq.L) is the kth element of the ascending sequence e; and then the odd sequence [ o ] with the length of L₁,o₃,...,o_2L-1]And a sequence of length L e ═ e₁,e₂,...,e_L]Merging by using an odd-even merger to obtain a ascending sequence [ p ] with the length of 2L₁,p₂,...,p_2L]，p_k(1. ltoreq. k.ltoreq.2L) is the kth element of the ascending sequence; will satisfy p₁≤p₂≤...≤p_LCandidate path metric value p₁,p₂,...p_L]As candidate path and path metric value of the ith layer

2. Channel polarization decoding circuit as claimed in claim 1The path metric value ordering method is characterized in that the parent path metric value of the ith layer path expansion is

And p is_i-1To ascending sequence, satisfy

The ith candidate path metric value of the (i-1) th layer is represented.

3. The method of claim 1 wherein the path metric values are ordered for a parent path

Adding bits 0 and 1, respectively, expands into two new paths (u)₁,u₂,...,u_i-10) and (u)₁,u₂,...,u_i-1And 1), then L father paths are expanded into 2L son paths, and L is a natural number.

4. The method of claim 3, wherein the path metric values o-o for 2L sub-paths are sorted according to the path metric value o-o₁,o₂,...o_2L]Recursion formula according to path metric of Polar code of channel polarization code

In the formula, L_lFor computing i-th layer bits on the basis of the l-th parent path sequenceLikelihood probability, and L is more than or equal to 1 and less than or equal to L.

5. The method according to claim 1, wherein the channel polarization decoding path metric value sorting method is characterized in that the code length of the channel polarization code Polar is N, the Polar codes all correspond to a full binary tree with a depth of N, each layer edge of the full binary tree corresponds to an information bit or a fixed bit, edges between each node and its left and right two subsequent nodes are marked as 0 and 1, respectively, except for leaf nodes, and a decoder starts from a root node to any path with a leaf node length of N and corresponds to a decoding sequence with a fixed bit.

6. The method of claim 1, wherein the path metric values formed by the decoder from the root node to any one of the nodes correspond to a path metric value.

7. The method of claim 1, wherein the decoder extends the paths starting from the root node, and when each layer extends to the next layer, all the candidate paths are reserved when the candidate paths are less than or equal to L; when the candidate path is larger than L, carrying out sequencing pruning, and selecting L paths with small path metric values in the current layer, wherein L is called the search width; and after arriving at the leaf node layer, outputting the decoding sequences corresponding to the L paths as a decoding candidate sequence set according to the sequence of the metric values from small to large.

8. The method of claim 1, wherein the decoder performs layer 1 edge expansion using a root node as a search starting point, and the two candidate paths are 0 and 1; when the decoder is expanded at the layer 2, 2 candidate paths are expanded into 4 new paths, namely (0,0), (0,1), (1,0) and (1,1), and the path metric values are 0.13, 0.61, and + ∞; in layer 3 expansion, 2 candidate paths are expanded into 4 new paths, respectively (0,0,0), (0,0,1), (0,1,0), and (0,1,1), with path metric values of 0.92, 0.13, 1.35, and 0.61; in layer 4 expansion, 2 candidate paths are expanded into 4 new paths, respectively (0,0,1,0), (0,0,1,1) (0,1,1,0) and (0,1,1,1), with path metric values of 0.13, 0.86, 1.48 and 0.61.

9. The method of claim 1, wherein the path metric values of the sub-candidate paths are divided into odd and even sequences according to sequence numbers; path metric value o for 2L subpaths ═ o₁,o₂,...o_2L]Divided into odd sequences [ o ] by sequence number₁,o₃,...,o_2L-1]And even sequence [ o ]₂,o₄,...,o_2L](ii) a Peculiar sequence [ o₁,o₃,...,o_2L-1]Is that

To ascending sequence, satisfy

10. The method of claim 1, wherein the parity sequences are ordered from small to large according to a parity ordering network; pair sequence [ o ]₂,o₄,...,o_2L]And ordering from small to large according to a method of the odd-even ordering network, wherein the odd-even ordering network is constructed by adopting an odd-even merger.