Polarization code PSS-RF-SCL decoding method based on reliability function

Abstract

The invention particularly relates to a polarization code PSS-RF-SCL decoding method based on a reliability function. In order to reduce decoding complexity and abandon a traditional path splitting strategy based on a search set, a path splitting strategy based on a reliability function is provided, and according to the strategy, whether information bits need to be subjected to path splitting or not is judged through the value of the reliability function. Secondly, a pruning strategy depending on an auxiliary path metric value is provided, and a PSS-RF-SCL decoding method is provided on the basis of the two decoding strategies for reducing complexity. During decoding, information bits with reliability function values lower than a threshold value alpha are regarded as bits needing path splitting, and paths with auxiliary path metric values higher than a threshold value beta are regarded as unreliable paths to be pruned. The threshold value alpha and the threshold value beta are obtained through statistical experiments. A simulation result shows that compared with a traditional path splitting strategy auxiliary SCL decoding method based on a search set, the provided PSS-RF-SCL decoding method has the advantage that the decoding complexity is obviously reduced on the premise of no performance loss.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel coding, and relates to an improvement of a decoding method of polar code in channel coding based on a path splitting selection strategy (Path Splitting Selecting strategy based on Search Set under the Successive Cancellation List, PSS-SS-SCL). The method mainly improves the PSS-SS-SCL decoding method through a path splitting strategy based on a reliability function and a pruning strategy based on an auxiliary path metric (APM). Background Art

[0002] Professor Arikan first proposed polar codes and proved that they can reach the Shannon limit of binary discrete memoryless symmetric channels. Today, polar codes have become a research hotspot in the field of channel coding due to their good performance, and have been adopted as the coding scheme for 5G control channels. While proposing polar codes, Professor Arikan also proposed a serial cancellation (SC) decoding method. The advantage of the SC decoding method is that there is no error floor. However, when the code length is limited, the performance of the SC decoding method is not ideal because the channel is not fully polarized and there is error propagation. To address this problem, some scholars have proposed a serial cancellation list (SCL) decoding method. This method increases the probability of obtaining a correct decoding result by retaining multiple decoding paths. In order to obtain better decoding performance, some scholars combined polar codes with check codes, and thus proposed a cyclic redundancy check code assisted serial cancellation list (Cyclic Redundancy Check Aid SCL, CA-SCL) decoding method. The cyclic redundancy check (CRC) code can select relatively correct decoding results from the decoding list in the final stage of decoding. The CA-SCL decoding method has good decoding performance and is the current mainstream decoding method. However, the CA-SCL decoding method has a large time and space complexity, so the CA-SCL decoding method has also become a method that is constantly being improved. Some scholars divide the information sequence into segments and perform CRC verification on each information sequence, thereby proposing a SCL (Segment CRC Aided SCL, SCA-SCL) decoding method based on segmented CRC. This method verifies each information sequence, prunes the incorrect decoding path, and can terminate the failed decoding process in advance, thereby reducing the decoding complexity.

[0003] Since the reliability of information bits is not completely consistent, in order to further reduce the complexity, some scholars proposed to perform path splitting only on unreliable information bits. On this basis, some scholars proposed the concept of search set, and constructed the search set using the partial order relationship of polarization channels. The search set contains most unreliable bits. The PSS-SS-SCL (Path Splitting Selecting strategy based on Search Set under the Successive Cancellation List) decoding method was proposed on this basis. The PSS-SS-SCL decoding method covers most unreliable bits by constructing a search set, and only performs path splitting on unreliable bits, thereby reducing the number of splitting times. Compared with the CA-SCL decoding method, the PSS-SS-SCL decoding method greatly reduces the decoding complexity with slightly reduced performance. However, in the PSS-SS-SCL decoding method, the number of split bits contained in the search set is greater than the number of bits that actually need to be path split, resulting in redundant splitting times, thereby increasing the decoding complexity. The existing SCL decoding methods that rely on the path splitting strategy to assist are all to select bits that need more path splitting in the search set, so as to achieve the purpose of reducing the number of splitting times. However, the effect of this method is not completely ideal. Therefore, a PSS-RF-SCL (Path Splitting Selecting strategy based on Reliability Function under the Successive Cancellation List) decoding method based on reliability function is proposed. In order to reduce the decoding complexity, this method abandons the search set and adopts a reliability function that is more in line with the actual decoding situation to select the bits that need to be path split. Compared with the path splitting strategy assisted SCL decoding method based on the search set, the PSS-RF-SCL decoding method significantly reduces the decoding complexity without reducing the decoding performance. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide a polar code PSS-RF-SCL decoding method based on reliability function. In order to reduce the decoding complexity, the method abandons the search set, judges whether the information bit needs to be path split by the value of the reliability function, and judges whether the path should be pruned by the APM value. With the help of the above strategy, the decoding method significantly reduces the number of unnecessary splits and the total number of decoding lists, and significantly reduces the decoding complexity without performance loss.

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

[0006] First, according to the actual transmission situation, a corresponding threshold value is obtained by statistical experiments. The information codeword is CRC-encoded and polarization-encoded to obtain a transmission codeword. The transmission codeword is placed in the channel for transmission.

[0007] Then, the transmitted codeword is decoded by SCL at the receiving end. Before the information bits are split into paths, the PM value of the path that meets the hard decision result is calculated. and the PM value of the path that does not meet the hard decision result use and Calculate the reliability function value E(i) of the bit. When E(i) is less than the threshold α, the path is split. When E(i) is greater than the threshold α, a hard decision is made directly. After an information bit is decoded, the APM value of each path is compared with β. Prune the path with an APM value greater than β.

[0008] Finally, the decoded codeword is subjected to CRC check. From the candidate paths that have successfully passed the CRC check, the path with the smallest PM value is selected. The codeword corresponding to the path is then determined as the final output codeword. If there is no codeword that has passed the CRC check, the decoding is declared a failure.

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

[0010] The present invention first proposes a path splitting strategy based on a reliability function and a pruning strategy relying on auxiliary path metrics. The path splitting strategy based on the reliability function is used to identify the split bits, which significantly reduces the number of redundant splits. The pruning strategy relying on auxiliary path metrics significantly reduces the total number of decoding lists. Based on these strategies, the proposed PSS-RF-SCL decoding method significantly reduces the decoding complexity compared to the traditional search set-based path splitting strategy-assisted SCL decoding method without performance loss. 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 It is a technical roadmap of the method of the present invention;

[0013] Figure 2 The block error rate performance comparison chart of five polar code decoding methods when the code length N = 1024, R = 1 / 2, L = 8;

[0014] Figure 3 The block error rate performance comparison chart of five polar code decoding methods when the code length N = 1024, R = 1 / 2, L = 16;

[0015] Figure 4 A comparison chart of the average number of decoding lists for five polar code decoding methods when the code length N = 1024, R = 1 / 2, and L = 8;

[0016] Figure 5 The figure is a comparison chart of the average splitting times of five polar code decoding methods when the code length N=1024, R=1 / 2, and L=8. DETAILED DESCRIPTION

[0017] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0018] (1) Combined with Figure 1 The specific implementation process of a polar code PSS-RF-SCL decoding method is as follows:

[0019] In the encoding stage, the information codeword Perform CRC encoding and polarization encoding to obtain the corresponding transmission codeword And set the corresponding thresholds α and β, Put it into the channel for transmission. Among them, the size of thresholds α and β needs to be obtained based on a large number of statistical experiments; the acquisition of threshold α requires statistics on the average reliability function value E(i) of hard decision error bits, and the size of this value is used as the size of threshold α; the acquisition of threshold β requires statistics on the APM distribution range of the correct decoding path, and the average APM of the correct decoding path is used as the size of threshold β; because the size of E(i) and the size of APM are both affected by the code length and signal-to-noise ratio, the present invention needs to obtain the thresholds α and β under different signal-to-noise ratios and code lengths through statistics; in the actual transmission process, the corresponding thresholds α and β are selected according to the actual transmission conditions.

[0020] In the decoding stage, SCL decoding is performed on the received codeword. i After the x (1≤x≤L) decoding paths are split, u i =1 and u i = 0, where x is the number of decoding paths that conform to u i The PM value of the path with hard decision result will remain unchanged. To indicate their PM values. i The PM value of the path with hard decision result will be larger. To represent their PM values. For the lth decoding path, from u 1 to u i The probability of no decoding error is approximately So the information bit u iWhether path splitting is needed is determined by the ratio of the total probability of x paths that meet the hard decision result to the total probability of x paths that do not meet the hard decision result, as shown in formula (1).

[0021]

[0022] When the ratio C is large, it means that the path reliability generated by the split in the bit is weaker than the original path reliability. i The less path splitting is needed, the smaller the u value is, the i Perform path splitting; in order to judge u by the threshold i The size of the ratio requires that the ratio has a suitable distribution range. However, the distribution range of the ratio obtained by formula (1) is too large and is not suitable for threshold judgment. Therefore, formula (1) is rewritten as the reliability function of formula (2):

[0023]

[0024] For information bit u i , if E(i)<α, path splitting is performed, otherwise hard decision decoding is performed.

[0025] The traditional PSS-SS-SCL decoding method is to reduce the decoding complexity by distinguishing the reliability of bits and using different decoding methods. However, the reliability of the specific path is not considered in the decoding process. There is no early pruning of completely unreliable paths, resulting in redundant decoding paths. In SCL decoding, the reliability of the path is measured by the PM value. However, the PM value is more suitable for selecting a path with higher reliability among all paths, but not for judging whether an error has occurred in the path. Therefore, the size of the APM value is used as the basis for whether an error has occurred in the path. The APM is only accumulated at the split bit, and remains unchanged at the frozen bit and other information bits. The calculation of APM is shown in formula (3).

[0026]

[0027] Among them, A S Represents the set of all split bits. Represents the information bit u i The APM distribution range of the correct path is much smaller than that of the PM. If the APM value of a path exceeds the threshold β, it can be regarded as an erroneous path and pruned.

[0028] Finally, the decoded codeword is subjected to CRC check. From the candidate paths that have successfully passed the CRC check, the path with the smallest PM value is selected. The codeword corresponding to the path is then determined as the final output codeword. If there is no codeword that has passed the CRC check, the decoding is declared a failure.

[0029] (2) Combined with attachment Figure 2 , 3, 4, 5 illustrate the superiority of the method of the present invention, the simulation is as follows:

[0030] The PSS-SS-SCL decoding method is a scheme proposed in the literature [1] "GAO C, LIU RK, DAI B, et al. Path splitting selecting strategy-aided successive cancellation list algorithm for polar codes [J]. IEEE Communications Letters, 2019, 23 (3): 422-425."

[0031] The PSD-SCL GA decoding method and the PSD-SCL SA decoding method are the schemes proposed in the literature [2] "WANG XM, ZHANG HC, LIJ, et al. An Improved Path Splitting Decision-Aided SCL Decoding Algorithm for Polar Codes[J]. IEEE Communications Letters, 2021, 25(11): 3463-3467."

[0032] The CA-SCL decoding method is a scheme proposed in the literature [3] "NIU K, CHEN K. CRC-aided decoding of polarcodes[J]. IEEE Communications Letters, 2012, 16(10): 1668-1671."

[0033] In order to compare the performance of each method fairly, the same code length N, code rate R, maximum list number L are set for different methods in the simulation, and the length of the check code added in each method is the same. Each method uses the GA construction method with SNR = 2.5dB and BPSK modulation, and the channel uses the AWGN channel.

[0034] exist Figures 2-3The block error rate comparison diagram when the code length N = 1024, the code rate R = 1 / 2, and the maximum number of lists L = 8 and L = 16 is shown in. All methods add a 16-bit CRC check code at the end of the information sequence. When L = 8, the PSS-RF-SCL decoding method proposed in the present invention has the same performance as the PSS-SS-SCL and PSD-SCL GA decoding methods. The PSS-RF-SCL decoding method has only a small performance loss compared with the CA-SCL decoding method, but its decoding complexity is greatly reduced. And the PSS-RF-SCL decoding method has less performance loss than the more complex PSD-SCL SA decoding method. The proposed method has more advantages when the number of lists is large. When L = 16, the performance of the PSS-RF-SCL decoding method is better than that of PSS-SS-SCL and two different PSD-SCL decoding methods.

[0035] The decoding complexity of the SCL decoder is mainly related to the total number of decoding lists used in the decoding process and the number of split bits. Therefore, the present invention compares the complexity of each method from the above two aspects. The calculation method of the average number of decoding lists is shown in formula (4).

[0036]

[0037] Where T is the number of received decoding sequences, L i is the total number of times the i-th sequence in the received sequence is successfully decoded, is the number of decoding lists when the i-th sequence in the accepted sequence fails j times.

[0038] When comparing the complexity, each method sets the code length N=1024, the code rate R=1 / 2, the number of lists L=8, and adds a 16-bit check code.

[0039] from Figure 4 It can be seen that compared with the traditional PSS-SS-SCL and CA-SCL decoding methods, the total number of decoding lists of the PSS-RF-SCL decoding method decreased by 37% when the signal-to-noise ratio was 2.5dB, and decreased by 70% when the signal-to-noise ratio was 3dB. Compared with the less complex PSD-SCL GA decoding method, the total number of decoding lists of the PSS-RF-SCL decoding method also decreased by 44% when the signal-to-noise ratio was 3dB. Compared with the more stringent PSD-SCL SA decoding method, it decreased by 24% when the signal-to-noise ratio was 3dB.

[0040] Depend on Figure 5It can be seen that the number of splits of the PSS-RF-SCL decoding method is 80 when the signal-to-noise ratio is 1dB, which is 85% lower than that of the CA-SCL decoding method and 33% lower than that of other search set-based path splitting strategy-assisted SCL decoding methods. When the signal-to-noise ratio is 3dB, the number of splits of the PSS-RF-SCL decoding method is 8.3, which is 45% lower than that of the PSD-SCL GA decoding method. Although the number of splits of the PSD-SCL SA decoding method is basically the same as that of the proposed method when the signal-to-noise ratio is 3dB, its performance is obviously inferior to that of the PSS-RF-SCL decoding method.

[0041] In summary, the proposed method of the present invention significantly reduces the decoding complexity while maintaining the decoding performance not lower than that of the PSS-SS-SCL decoding method. In terms of both the number of splits and the total number of decoding lists, the proposed method is significantly lower than the existing search set-based path splitting strategy-assisted SCL decoding method. In addition, when the number of lists is large, the proposed method still has certain performance advantages.

Claims

1. A PSS-RF-SCL (Path Splitting Selecting strategybased on Reliability Function under the Successive Cancellation List) decoding method for polar codes based on reliability function. The method first proposes a path splitting strategy based on reliability function, which determines whether information bits need to be path split by the value of reliability function. Secondly, a pruning strategy based on auxiliary path metric (APM) is proposed. Based on the above two decoding strategies for reducing complexity, a PSS-RF-SCL decoding method is proposed. During decoding, the path metric (PM) values ​​that meet the hard decision results and the PM values ​​that do not meet the hard decision results in all paths are calculated, and the reliability function values ​​of the bits are calculated using these PM values. Information bits with reliability function values ​​lower than a threshold α are regarded as bits that need to be path split. In addition, paths with APM values ​​higher than a threshold β are regarded as unreliable paths and pruned. The values ​​of the thresholds α and β are obtained through statistical experiments. The decoding method specifically includes the following steps: Step 1: In the encoding stage, the information codeword Perform CRC encoding and polarization encoding to obtain the corresponding transmission codeword And set the corresponding thresholds α and β, Put it into the channel for transmission; the specific description of the thresholds α and β is as follows: The values ​​of thresholds α and β need to be obtained based on a large number of statistical experiments; the threshold α needs to be obtained by counting the average reliability function value E(i) of the hard decision error bit, and the value of this value is used as the value of threshold α; the threshold β needs to be obtained by counting the APM distribution range of the correct decoding path, and the average APM value of the correct decoding path is used as the value of threshold β; because the value of E(i) and the value of APM are both affected by the code length and signal-to-noise ratio, it is necessary to obtain the thresholds α and β under different signal-to-noise ratios and code lengths through statistics; in the actual transmission process, the corresponding thresholds α and β are selected according to the actual transmission conditions; Step 2: In the decoding stage, SCL decoding is performed on the received codeword; When u i After the x (1≤x≤L) decoding paths are split, u i =1 and u i = 0, where x is the number of decoding paths that conform to u i The PM value of the hard decision path will remain unchanged. To indicate their PM value; for those that do not meet u i The PM value of the path with hard decision result will be larger. To indicate their PM values; For the lth decoding path, from u1 to u i The probability that no decoding error occurs is approximately So the information bit u i Whether path splitting is needed is determined by the ratio of the total probability of x paths that meet the hard decision result to the total probability of x paths that do not meet the hard decision result, as shown in formula (1); When the ratio C is large, it means that the path reliability generated by the split in the bit is weaker than the original path reliability. i The less path splitting is needed, the smaller the u value is, the i Perform path splitting; in order to judge u by the threshold i The ratio of needs to have a suitable distribution range; however, the ratio distribution range obtained by formula (1) is too large and is not suitable for threshold judgment; therefore, formula (1) is rewritten as the reliability function of formula (2): For information bit u i , if E(i)<α, path splitting is performed, otherwise hard decision decoding is performed; The traditional PSS-SS-SCL (Path Splitting Selecting strategy based on Search Setunder the Successive Cancellation List) decoding method uses different decoding methods to reduce the decoding complexity by distinguishing the reliability of bits. However, the reliability of specific paths is not considered during the decoding process. Completely unreliable paths are not pruned in advance, resulting in redundant decoding paths. In SCL decoding, the PM value is used to measure the reliability of the path. However, the PM value is more suitable for selecting a path with higher reliability among all paths, rather than for determining whether an error has occurred in the path. Therefore, the size of the APM value is used as the basis for whether the path has an error. APM is only accumulated at the split bit, and remains unchanged at the frozen bit and other information bits. The calculation of APM is shown in formula (3); Among them, A S represents the set of all split bits; Represents the information bit u i The estimated value of the correct path is much smaller than the PM. If the APM value of a path exceeds the threshold β, it is regarded as an erroneous path and pruned. Step 3: Finally, perform CRC check on the decoded codeword. From the candidate paths that successfully pass the CRC check, select the path with the smallest PM value. The codeword corresponding to the path is then determined as the final output codeword. If there is no codeword that passes the CRC check, the decoding is declared a failure.

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