Partitioned CRC polar code SCLF decoding method based on CS segmentation

Abstract

The invention relates to a partition CRC polar code SCLF decoding method based on CS segmentation. According to the method, a polarization code is divided into a plurality of partitions according to the cumulative probability of a first error of an information bit in a CS, error bits of each partition are checked, identified and flipped by using a CRC code, the flipping precision is improved, the number of times of re-decoding is reduced, in addition, in order to improve the competitiveness of a correct path, a path pruning operation is added during decoding, and the decoding efficiency is improved. And the decoding bit number is reduced by terminating the decoding process operation in advance. A simulation result shows that compared with a DPost-SCLF decoding method, a PSCLF decoding method and a DPC-SCLF decoding method, the decoding performance of the PCS-SCLF decoding method provided by the invention is improved to a certain extent.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel coding, and relates to a partitioned cyclic redundancy check (CRC) polar code SCLF (Partitioned CRC Successive-Cancellation List Flip Decoding of Polar Codes based on Critical Set segmentation, PCS-SCLF) decoding method based on critical set (CS) segmentation in channel coding. The method divides the polar code into multiple partitions according to the cumulative probability of the first error of the index in the CS, and uses the CRC code to check, identify and flip the error bit of each partition. In addition, in order to improve the competitiveness of the correct path, a path pruning operation is added during decoding, and the decoding process operation is terminated in advance to reduce the number of decoding bits. Background Art

[0002] Polar codes have been used as the coding standard for control channels in 5G enhanced mobile broadband scenarios due to their superiority. The serial cancellation (SC) decoding method of polar codes can reach the channel capacity when the code length is infinite, but for the SC decoding method with medium and short code lengths, serious error propagation will occur during the decoding process, resulting in poor error performance.

[0003] In order to improve the polar code decoding method, scholars proposed a cyclic redundancy check aided SCL (CA-SCL) decoding method. This method cascades a cyclic redundancy check (CRC) code at the end of the polar code, and verifies multiple candidate paths through the CRC code, effectively improving the performance of the polar code decoding method. In order to improve the error performance of the CA-SCL decoding method, scholars proposed a serial cancellation list bit flip (SCLF) decoding method. This method combines the CA-SCL decoding method and the SCF decoding method well, and the error performance is also greatly improved over CA-SCL and SCF. SCLF decoding achieves flipping by changing the path competition decision result of the flipped bit during the re-decoding process. In order to improve the performance of the initial SCLF decoding method, scholars proposed an advanced decision post-processing (D-Post) flipping criterion, and based on this criterion, proposed a high-order SCLF decoding method with multiple bit flips. Taking into account the problem of high complexity of the existing SCLF decoding method, the present invention proposes a CS-segmented partitioned CRC polar code SCLF (Partitioned Cyclic Redundancy Check Successive-Cancellation List Flip Decoding of Polar Codes based on Critical Set segmentation, PCS-SCLF) decoding method which can reduce the number of re-decoding times and the number of decoding bits. The method reduces the complexity of SCLF decoding and improves the error performance within a certain range. Summary of the invention

[0004] In view of this, the object of the present invention is to provide a partitioned CRC polar code SCLF decoding method based on CS segmentation. The method divides the polar code into multiple partitions according to the cumulative probability of the first error in the index in the CS, and uses the CRC code to check, identify and flip the error bit of each partition. In addition, in order to improve the competitiveness of the correct path, a path pruning operation is added during decoding, and the decoding process operation is terminated in advance, which effectively improves the probability that the correct path is retained until the end of decoding, reduces unnecessary decoding processes, and thus reduces decoding complexity.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] Firstly, CS is constructed according to the partial order relationship of polarization channels. CS is composed of the index of the worst polarization channel in the special node R1 code in the polar code. The CS in the SCL decoding method contains most of the decoding error bits caused by channel noise. E is used to represent the random variable describing the first error in the CS set in the SCL of the polar code. The cumulative error probability F(k) of E is calculated, and the information sequence is divided into P partitions according to F(k).

[0007] Then, the special relationship between adjacent R1 codes of different lengths and the occurrence of decoding errors is analyzed. When there are two consecutive R1 code sub-blocks A and B, and the B sub-block is larger, the probability of deletion errors in the B sub-block is greater than that in the A sub-block, and the longer the length of the B sub-block, the greater the probability of two or more errors. According to this special relationship, the initial flip set IFS is constructed. The decoding process of the partitioned CRC polar code will be terminated in advance when the decoding fails, so all position indexes in the IFS are not required. When the SCL decoding reaches the position index bit μ for the first time, p After the bits are added, only when no path satisfies the CRC check, the information bits belonging to partition p (1≤p≤P) in IFS are constructed into the partition flip set PFS of the PCS-SCLF decoding method.

[0008] Finally, SCL decoding is performed on P partitions in sequence. For a partition where a CRC code is located, a CRC check is performed after the decoding of the partition is completed. If there is a decoding sequence that passes the CRC check, the paths that do not pass the CRC check are pruned and only the paths that pass the CRC check and have the smallest path metric (PM) value are selected to continue the decoding of the next partition; if all sequences fail the CRC check, the decoding process is terminated in advance, and then a flip set PFS is constructed for re-decoding, and the bits in the PFS are flipped sequentially. If the re-decoding process successfully passes the final CRC check, the correct decoding path is output, otherwise the next re-decoding is performed. When the maximum number of flips is reached and the correct decoding sequence has not been obtained, the decoding is declared a failure.

[0009] The beneficial effects of the present invention are:

[0010] The flip set and partition CRC structure constructed by the present invention can effectively narrow the search range of decoding error bits, accurately locate the positions of error bits, improve error performance, and reduce the number of re-decoding times. At the same time, the early termination of the decoding process is integrated into the decoding process, which reduces the number of decoding bits and reduces the decoding complexity. The path pruning operation in the decoding method can effectively reduce the competition of the error path for the correct path and improve the probability that the correct path is retained until the end of decoding. The simulation results show that the PCS-SCLF decoding method proposed in the present invention can more accurately identify the first error bit caused by channel noise than the DPC-SCLF decoding method in the literature [1] "Yuan Jianguo, He Jingjie, Zhang Fengguo, et al. Low-complexity polar code SCLF decoding method based on distributed parity check code [J]. Semiconductor Optoelectronics, 2023, 44(06): 931-937."; compared with the DPost-SCLF decoding method in the literature [2] "WANG Zhongxuan, PAN Yihan, LIN Yuheng. Post-processing for CRC-aided successive cancellation list decoding of polar codes [J]. IEEE Communications Letters. 2020, 24(7): 1395-1399.", the path pruning and early termination of the decoding process in the PCS-SCLF decoding method can effectively reduce unnecessary re-decoding processes and obtain better error performance and lower complexity; compared with the literature [3] "Pillet C, Sagitov I, Domer G, et al. al.Partitioned Successive-Cancellation List Flip Decoding of Polar Codes[J].arXiv preprintarXiv:2409.00266,2024." The PSCLF decoding method in the proposed partitioned CRC structure can better improve the verification capability of the check code, thereby increasing the probability that the correct path is retained until the end of decoding, thereby improving the decoding performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0012] Figure 1 A technical roadmap for the method of the present invention;

[0013] Figure 2 It is a schematic diagram of CS;

[0014] Figure 3It is a curve diagram of the cumulative error probability F(k) of the first error E occurring in the CS position at different signal-to-noise ratios;

[0015] Figure 4 It is the block error rate curve diagram of different decoding methods;

[0016] Figure 5 The block error rate curve of the PCS-SCLF decoding method ablation experiment;

[0017] Figure 6 It is a curve chart of average decoding times for different decoding methods; DETAILED DESCRIPTION

[0018] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0019] (1) Combined with Figure 1 The specific implementation process of a partitioned CRC polar code SCLF decoding method based on CS segmentation is as follows:

[0020] Step 1: Construct CS according to the partial order relationship of polarization channels. CS is composed of the index of the worst polarization channel in the special node R1 code in the polar code. The CS in the SCL decoding method contains most of the decoding error bits caused by channel noise. E is used to represent the random variable describing the first error in the CS of the polar code. Assume that the code length of the polar code is N = 2 n , the message length is K, and the SCL decoder with a list size of L is used for decoding. E only appears in {i log2L+1 ,i log2L+2 ,...,i K}, the cumulative density function (CDF) of E is expressed as F(k), and the definition of F(k) is shown in formula (1).

[0021]

[0022] There is a relationship between channels as shown in formula (2), where represents statistical degradation, e.g. Channel W is called the statistical degradation of channel Q, and P e (W)≥P e (Q).

[0023]

[0024] Channel Error Probability It is obtained by formula (3), where For Channel The mean of the logarithm likelihood ratio (LLR).

[0025]

[0026] in erfc(x) is the complementary error function,

[0027] In the Gaussian Approximation (GA) construction, the source bits are modulated by Binary Phase Shift Keying (BPSK) i =1-2x i , assuming that the source bits are all 0 bits, then the sequence sent by BPSK is a sequence of all 1s, and each received BPSK symbol is y i =1+n i , where n i is additive Gaussian white noise with a mean of 0 and a variance of σ 2 , so y i Also a random variable y that follows a Gaussian distribution i ~N(1,σ 2 ), BPSK modulation is used in the additive white Gaussian noise (AWGN) channel, and the calculation formula of the i-th LLR is shown in formula (4).

[0028]

[0029] Formula (4) shows that the value of LLR is related to the noise power σ 2 Inversely proportional, when the noise power increases, the LLR value decreases and the channel error probability increases. The channel in CS becomes less reliable as the noise increases, and the error probability increases. The probability of the first error occurring earlier in CS increases with the increase of noise. Monte Carlo simulation experiments are used to count the probability of the first error occurring for each element in CS and calculate the CDF F(k) of each position.

[0030] Step 2: Partition CRC polar code is divided into P (P>1) partitions, each partition should contain K p (K p >1) information bits, and its size is C p The number of information bits and the number of CRC bits are and s p represents the number of non-frozen bits in the pth partition, s p =K p +C p, the cumulative number of non-frozen bits is denoted as S p , In the codeword sequence, the last index of each partition is stored in μ = {μ1,μ2,...,μ P}, the partition CRC design is to evenly distribute the partitions according to CDFF(k), and the partition rule is shown in formula (5).

[0031]

[0032] Step 3: Assume that there are two consecutive R1 code sub-blocks A and B, and record the event in which the correct path on sub-block A is deleted as E A Similarly, the event that the correct path on sub-block B is deleted is recorded as E B , E A With E B There is a relationship shown in formula (6).

[0033]

[0034] where p α is an optimized probability function.

[0035] In SCL decoding, if sub-block A is preceded by an R1 code with a smaller block length, sub-block A is not very reliable due to accumulated errors. Therefore, in SCL decoding, the probability of two or more errors in the R1 code with a larger block length is very high. According to the partial order relationship of the polar code channel, if the R1 code length is greater than or equal to 8, the first, second, and third position indexes of the R1 code are added to the initial flip set (Initial Flip Set, IFS). When the R1 code length is less than 8, only the first position index needs to be added to the IFS. The decoding process of the partitioned CRC polar code will terminate the decoding process in advance when the decoding fails, so it is not necessary to flip all the position indexes in the set. When the SCL decoding reaches the position index μ for the first time, p After the bits are added, only when all paths do not satisfy the CRC check, the information bits belonging to partition p (1≤p≤P) in IFS are constructed into a partitioned flip set (PFS) of the PCS-SCLF decoding method. The construction of PFS is shown in formula (7).

[0036] PFS={i|IFS(i),μ p-1 ≤i≤μ p} (7)

[0037] Step 4: Since the partition CRC structure divides the information sequence into P partitions, the PCS-SCLF decoding process will be divided into P processes, and p (1≤p≤P) is used to represent the decoding sequence of the pth partition. This method performs SCL decoding on each partition in sequence. For the pth partition, a CRC check is performed after the decoding of the partition is completed. If there is a decoding sequence that passes the CRC check, the paths that do not pass the CRC check are pruned, and only the paths that pass the CRC check and have the smallest PM value are selected to continue the decoding of the next partition; if all paths fail the CRC check, the decoding process is terminated in advance, and then a flip set PFS is constructed for re-decoding. The bits in the PFS are flipped in the order of the positions in the PFS. If the re-decoding process successfully passes the final CRC check, the correct decoding path is output, otherwise the next re-decoding is performed. When the maximum number of flips is reached and the correct decoding sequence is not obtained, the decoding is declared failed.

[0038] (2) Combined with attachment Figure 2 Explain the construction method of CS:

[0039] CS consists of the index of the worst polarization channel in the corresponding R1 code in the polar code. Figure 2 The polar code with code length N=8 and A={4,6,7,8} is shown. The black nodes indicate that all its leaf nodes are information bits, the white nodes indicate that all its leaf nodes are frozen bits, the gray nodes indicate that its leaf nodes have both information bits and frozen bits, the solid rectangular box indicates the sub-polar code with code rate 1, and the bit index in the dashed rectangular box constitutes CS, which is denoted as CS={4,6,7}.

[0040] (3) Combined with attachment Figure 3 The selection of the partition CRC scheme is described as follows:

[0041] Let E represent the random variable describing the first error in the CS set in the SCL decoding method of the polar code, and the CDF of E is denoted as F(k), Figure 3 The list size is L=8, and the signal-to-noise ratio is E. b / N0={1,1.5,2,2.5}(dB) F(k) curve, according to Figure 3 show, The probability of the first error occurring early in the partition increases with the increase of noise. The partition CRC design is based on the uniform distribution of the partitions according to CDF F(k). When the signal-to-noise ratio is too small, the first error occurs in the first half of the CS. On the contrary, when the signal-to-noise ratio is too large, the first error occurs in the first half of the CS. Selecting F(k) to partition the information sequence when the signal-to-noise ratio is too small or too large will lead to extremely uneven information bits in the partitions. Therefore, the signal-to-noise ratio E is selected. bWhen / N0=2dB, F(k) partitions the information sequence, and the set μ is μ={360,458,615,1024}.

[0042] (5) Combined with attachment Figure 4 , 5, 6 illustrate the superiority of the method of the present invention, the simulation is as follows:

[0043] In order to verify the superiority of the method proposed in the present invention, the error performance and complexity of the PCS-SCLF decoding method are simulated and analyzed. The simulation conditions are: the polar code length N = 1024, the code rate R = 0.5, the list size L = 8, the codeword is BPSK modulated and transmitted under the AWGN channel, the Gaussian approximation construction method with a signal-to-noise ratio SNR = 2.5dB is used, the non-partitioned CRC polar code decoding method CRC check code length r = 16, and the CRC check code generator polynomial is g 16 (x) = x 16 +x 15 +x 2 +1, the partition CRC method sets P to 4, the total length of the CRC check code is r = 16, then the CRC check code generator polynomial is g4(x) = x 4 +x+1, the number of simulation iterations is 10 6 , the maximum number of flips for all decoding methods is set to T max =50.

[0044] The PCS-SCLF decoding method proposed in the present invention is compared with the CA-SCL decoding method in the document [4] "NIU Kai, CHEN Kai. CRC-aided decoding of polar codes [J]. IEEE Communications Letters, 2012, 16 (10): 1668-1671.", the DPC-SCLF decoding method in the document [1], the DPost-SCLF decoding method in the document [2] and the PSCLF decoding method in the document [3], and the block error rate and average decoding times of the above methods are analyzed.

[0045] In order to further verify the superiority of the pruning strategy and the constructed flip set, the PCS-SCLF decoding method was subjected to an ablation experiment. When the pruning strategy was not used, a CRC check was performed on the information in a partition immediately after the decoding of the partition was completed. If there were branches that passed the check, only the branches that did not pass the CRC check were pruned, and all paths that passed the CRC check were retained. When PFS was not used, CS was directly used as the flip set of the SCLF decoding method.

[0046] Depend on Figure 4The results show that the PCS-SCLF decoding method has better error performance than other decoding methods. -4 When , the PCS-SCLF decoding method has gains of 0.2dB, 0.08dB, 0.09dB, 0.26dB, and 0.1dB respectively compared with the DPost-SCLF decoding method, PSCLF decoding method, DPC-SCLF decoding method, and CA-SCL decoding method with list size L=8 and 16. The ablation experiment results are shown in Figure 5 As shown, "w / o" means without, Figure 5 It can be obtained that the error performance of the PCS-SCLF decoding method is better than that of the SCLF decoding method without using the pruning strategy and the constructed flip set, which proves that the pruning strategy and the constructed flip set proposed in the present invention have certain advantages in the partitioned CRC polar code.

[0047] The computational complexity of the bit flipping method is described as the average number of decoding times. The higher the average number of decoding times, the higher the computational complexity. The complexity of the CA-SCL decoder is normalized to 1 when the list size L = 8. The complexity of each decoding method is as follows: Figure 6 As shown by Figure 6 It shows that the PCS-SCLF decoding method has lower complexity than other SCLF decoding methods. When the signal-to-noise ratio is 1 dB, the complexity of the PCS-SCLF decoding method is 39.4%, 9.2%, and 33.6% lower than that of the DPost-SCLF decoding method, the PSCLF decoding method, and the DPC-SCLF decoding method. Therefore, the PCS-SCLF decoding method proposed in the present invention has low complexity and good error correction performance.

Claims

1. A partitioned cyclic redundancy check (CRC) polar code SCLF (Partitioned CRC Successive-Cancellation List Flip Decoding of Polar Codes based on Critical Set segmentation, PCS-SCLF) decoding method based on critical set (CS) segmentation. Aiming at the problem of high complexity of polar code SCLF decoding method, the method divides the polar code into multiple partitions according to the cumulative probability of the first error of the information bit in CS. In the decoding process, the partition CRC structure partitions the decoding sequence so that the CRC code can fully check the decoding path, prune the path that fails the CRC check and only selects the path that passes the CRC check and has the smallest path metric (PM) value, thereby improving the probability that the correct path is retained until the end of decoding. At the same time, the early termination of the decoding process is integrated into the decoding process, and the decoding process of all paths that fail the CRC check is terminated in advance, which effectively reduces the number of decoding bits in the entire decoding process. The specific steps of the method are as follows: Step 1: Construct CS according to the partial order relationship of polarization channels. CS consists of the index of the worst polarization channel in the special node R1 code in the polar code. The CS in the serial cancellation list (SCL) decoding method contains most of the decoding error bits caused by channel noise. E is used to represent the random variable describing the first error in the CS of the polar code. Assume that the code length of the polar code is N = 2 n , the message length is K, and the SCL decoder with a list size of L is used for decoding. E only appears in {i log2L+1 ,i log2L+2 ,...,i K } position, the Cumulative Density Function (CDF) of E is expressed as F(k), and the definition of F(k) is shown in formula (1); There is a relationship between channels as shown in formula (2), where "<" indicates statistical degradation, for example, W<Q, which means that channel W is the statistical degradation of channel Q, and P e (W)≥P e (Q); Channel Error Probability It is obtained by formula (3), where For Channel The mean of the logarithm likelihood ratio (LLR); in erfc(x) is the complementary error function, In the Gaussian Approximation (GA) construction, the source bits are modulated by Binary Phase Shift Keying (BPSK) i =1-2x i , assuming that the source bits are all 0 bits, then the sequence sent by BPSK is a sequence of all 1s, and each received BPSK symbol is y i =1+n i , where n i is additive Gaussian white noise with a mean of 0 and a variance of σ 2 , so y i Also a random variable y that follows a Gaussian distribution i ~N(1,σ 2 ), using BPSK modulation in the additive white Gaussian noise (AWGN) channel, the calculation formula of the i-th LLR is shown in formula (4); Formula (4) shows that the value of LLR is related to the noise power σ 2 Inversely proportional, when the noise power increases, the LLR value decreases and the channel error probability increases. The channel in CS becomes less reliable as the noise increases, and the error probability increases. The probability of the first error occurring earlier in the CS increases with the increase of noise. Monte Carlo simulation experiments are used to count the probability of the first error occurring in each element of the CS and calculate the CDF F(k) of each position. Step 2: Partition CRC polar code is divided into P (P>1) partitions, each partition should contain K p (K p >1) information bits, and its size is C p The number of information bits and the number of CRC bits are and s p represents the number of non-frozen bits in the pth partition, s p =K p +C p , the cumulative number of non-frozen bits is denoted as S p , In the codeword sequence, the last index of each partition is stored in μ = {μ1,μ2,...,μ P }, the partition CRC design is to evenly distribute the partitions according to CDFF(k), and the partition rule is shown in formula (5); Step 3: Assume that there are two consecutive R1 code sub-blocks A and B, and record the event in which the correct path on sub-block A is deleted as E A Similarly, the event that the correct path on sub-block B is deleted is recorded as E B , E A With E B There is a relationship as shown in formula (6); where p α is an optimized probability function; In SCL decoding, if sub-block A is preceded by an R1 code with a smaller block length, sub-block A is not very reliable due to accumulated errors. Therefore, in SCL decoding, the probability of two or more errors in the R1 code with a larger block length is very high. According to the partial order relationship of the polar code channel, if the R1 code length is greater than or equal to 8, the first, second, and third position indexes of the R1 code are added to the initial flip set (Initial Flip Set, IFS). When the R1 code length is less than 8, only the first position index needs to be added to the IFS. The decoding process of the partitioned CRC polar code will terminate the decoding process in advance when the decoding fails, so it is not necessary to flip all the position indexes in the set. When the SCL decoding reaches the position index μ for the first time, p After the bits are counted, only when all paths do not satisfy the CRC check, the information bits belonging to partition p (1≤p≤P) in IFS are constructed into a partitioned flip set (PFS) of the PCS-SCLF decoding method. The construction of PFS is shown in formula (7); PFS={i|IFS(i),µ p-1 ≤i≤µ p } (7) Step 4: Since the partition CRC structure divides the information sequence into P partitions, the PCS-SCLF decoding process will be divided into P processes, and p (1≤p≤P) is used to represent the decoding sequence of the pth partition. This method performs SCL decoding on each partition in sequence. For the pth partition, a CRC check is performed after the decoding of the partition is completed. If there is a decoding sequence that passes the CRC check, the paths that do not pass the CRC check are pruned, and only the paths that pass the CRC check and have the smallest PM value are selected to continue the decoding of the next partition; if all paths fail the CRC check, the decoding process is terminated in advance, and then a flip set PFS is constructed for re-decoding. The bits in the PFS are flipped in the order of the positions in the PFS. If the re-decoding process successfully passes the final CRC check, the correct decoding path is output, otherwise the next re-decoding is performed. When the maximum number of flips is reached and the correct decoding sequence is not obtained, the decoding is declared failed.

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