A polar code SCLF decoding method based on specific set and dynamic LLR threshold decision improvement

Abstract

This invention specifically relates to an improved polar code successive cancellation list bit-flipping (SCLF) decoding method based on an assigned set (AS) and a dynamic logarithm likelihood ratio (LLR) threshold. This method first constructs an AS set using path metric (PM) information from Cyclic Redundancy Check Aided Successive Cancellation List (CA-SCL) decoding. Then, it performs a secondary selection of the AS set using a dynamic LLR threshold based on the code length and the maximum number of flips. Simulation results show that this method improves decoding performance and effectively reduces the average number of decoding operations in low signal-to-noise ratio regions, achieving optimization of both decoding performance and computational complexity.

Description

Technical Field

[0001] This invention belongs to the field of channel coding technology and relates to a polar code successive cancellation list bit-flipping (SCLF) decoding method based on an improved decision using an assigned set (AS) and a dynamic logarithm likelihood ratio (LLR) threshold. This method mainly combines path metric (PM) information from Cyclic Redundancy Check Aided Successive Cancellation List (CA-SCL) decoding to construct the AS set. A dynamic LLR threshold based on code length and the maximum number of flips is introduced to perform secondary filtering on the AS set. The strategy of only SC state nodes in the decoding tree being flippable is used to accurately locate potential error bits. By delaying the position of the first error bit, early path loss is reduced, achieving a good trade-off between improved decoding performance and reduced computational complexity. Background Technology

[0002] Polar codes, as the first error-correcting coding scheme rigorously proven to achieve Shannon capacity on binary-input discrete memoryless channels, have been adopted by 3GPP standards as the coding scheme for control channels in 5G enhanced mobile broadband (eMBB) scenarios due to their simple encoding and decoding structure and excellent error-correcting performance, becoming one of the key channel coding technologies in modern wireless communication systems.

[0003] Early proposed successive cancellation (SC) decoding algorithms, while approaching the Shannon limit as the code length approaches infinity, have a decoding complexity of only [missing information]. However, due to its serial decoding characteristic, errors in preceding bits propagate backwards, leading to suboptimal decoding performance with finite code lengths. To compensate for this deficiency, researchers proposed the Successive Cancellation List (SCL) decoding algorithm, which reduces the impact of error propagation by retaining L optimal decoding paths. When L is sufficiently large, its performance can approach that of Maximum Likelihood (ML) decoding. To further improve decoding reliability, the CA-SCL decoding algorithm was proposed, incorporating Cyclic Redundancy Check (CRC) into the path selection process, outputting only the optimal path that passes the check, effectively reducing the block error rate.

[0004] However, the performance improvement of SCL and CA-SCL decoding algorithms depends on increasing the path list L, which directly leads to a significant increase in decoding computational complexity, storage overhead, and decoding latency. The larger L is, the higher the cost of path sorting, storage, and expansion, making it difficult to meet the requirements of ultra-reliable low-latency communication (uRLLC) scenarios in 5G communication. To solve this problem, the SCLF decoding algorithm has emerged. Its core idea is to re-decode by flipping the potential error bits in the Critical Set (CS) when CA-SCL decoding fails, thereby improving error correction performance with fewer re-decoding attempts. Among the existing SCLF-related improved algorithms, the CS-based SCLF decoding algorithm uses the first bit of the Rate-1 node to form the CS set, reducing error propagation; the AS-based SCLF decoding algorithm identifies error bits through normalized confidence.

[0005] Although the above algorithms have optimized decoding performance to some extent, they still have significant shortcomings: the CS set of traditional SCLF algorithms is mostly statically constructed or relies on fixed channel reliability ordering, which cannot adapt to changes in dynamic channel noise, resulting in inaccurate error location, incomplete CS set, and some bits that need to be flipped not being included. The presence of redundant bits increases invalid re-decoding operations and increases the complexity of the algorithm.

[0006] To further improve the practicality of the SCLF decoding algorithm, the academic community has explored the construction and complexity optimization of dynamic CS sets: some studies have attempted to capture potential error bits through post-decision processing or introduce threshold mechanisms to improve the accuracy of key sets, but have failed to form a comprehensive solution that combines theoretical rigor and practical effectiveness.

[0007] Therefore, in response to the core problems of incomplete key sets, inaccurate error location, and high complexity in existing SCLF decoding algorithms, there is an urgent need for an optimization scheme that balances improved decoding performance with reduced complexity. This scheme should accurately locate erroneous bits and reduce invalid computations while maintaining good block error rate performance, so as to meet the requirements of 5G and future communication systems for highly reliable, low-latency, and low-complexity decoding. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide an improved SCLF decoding method based on AS set and dynamic LLR threshold decision. This method optimizes the flip set through a dual mechanism of "AS set construction + dynamic threshold filtering", accurately locates potential error bits, delays the occurrence of the first error bit to reduce early path loss, and achieves a good trade-off between decoding performance and computational complexity.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] First, construct the AS set and remove invalid flip positions. For a CA-SCL decoder with code length N, information length K, and list size L, after decoding failure, use the path metric (PM) value recorded during the decoding process to calculate the total probability A(i) of the eliminated path for each information bit according to equation (1), calculate the total probability B(i) of the retained path according to equation (2), and define the path decision confidence level according to equation (3). The theoretical confidence threshold C(i) obtained by combining the Gaussian approximation principle is shown in equation (4):

[0011] (1)

[0012] (2)

[0013] (3)

[0014] (4)

[0015] All information bits that satisfy the path decision confidence level below the theoretical confidence threshold are included in the AS set. This set focuses on bit positions where the decoder is prone to making erroneous decisions, thus initially narrowing down the range of flip candidates.

[0016] Then, a dynamic LLR threshold is designed to perform secondary filtering on the AS set. The auxiliary SC decoding is run once to obtain the dynamic LLR sequence of the current received sequence. Based on the code length N and the maximum number of flips T, the dynamic threshold is calculated using the threshold formula (5):

[0017] (5)

[0018] Using this threshold, the intersection of the AS sets is filtered to retain only those LLR amplitudes that meet the criteria. The bits are then sorted in ascending order of LLR amplitude to obtain an optimized flip candidate set, enabling accurate error location based on real-time channel information.

[0019] The beneficial effects of this invention are as follows:

[0020] This invention significantly improves decoding performance by using a dual screening process of the AS set and a dynamic threshold to accurately locate potential error bits and delay the position of the first error bit to reduce early path loss. It also offers strong flexibility; the dynamic threshold formula adapts to changes in code length and maximum number of flips, and the threshold decision mechanism can be extended to other SCLF decoding algorithms based on CS set modifications, making it suitable for the high-reliability, low-latency decoding requirements of 5G and future communication systems. Attached Figure Description

[0021] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0022] Figure 1 This is a technical roadmap of the method of the present invention;

[0023] Figure 2 A comparison chart of decoding block error rate performance under different thresholds;

[0024] Figure 3 A comparison of the block error rate performance of various polar code decoding methods when code length N=1024 and L=8;

[0025] Figure 4 This represents the average number of decoding splits for different decoding methods. Detailed Implementation

[0026] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0027] (1) Combined with appendix Figure 1 The following describes an improved polar code SCLF decoding method based on AS set and dynamic LLR threshold decision:

[0028] Step 1: Perform CA-SCL decoding. If a path passes the CRC check, output the path with the smallest path metric (PM) as the decoding result. If all paths fail the check, start bit-flipping re-decoding.

[0029] Step 2: Calculate the actual path decision confidence for each information bit using the PM information when CA-SCL decoding fails, and combine it with the channel theory threshold obtained from the Gaussian approximation. Include all satisfied bits in the AS set. Introduce dynamic threshold decision for elements in the AS set. Run auxiliary SC decoding to obtain the dynamic log-likelihood ratio (LLR) sequence of the current frame, and calculate the dynamic threshold based on the code length N and the maximum number of flips T. Then, sort the filtered bits according to the LLR magnitude. This completes the construction of the flip candidate set.

[0030] Step 3: Perform re-decoding according to the bit order of the optimized candidate set. During the re-decoding process, only nodes in the SC state (only one path is retained) in the decoding tree are flipped. Nodes in the clone state (both paths are retained) and the deletion state (both paths are eliminated) are not processed to avoid invalid flips. After each flip, PM is recalculated and CRC check is performed. If a path that passes the check is found within the maximum number of flips T, the decoding result with the smallest PM is output. If it fails, the path with the smallest PM in the first CA-SCL decoding is output.

[0031] (2) Combined with the appendix Figure 2 Explanation of the threshold decision formula:

[0032] The Successive Cancellation Flip (SCF) decoding algorithm improves performance by delaying the position of the first erroneous bit, thus delaying errors caused by channel noise. In SCLF decoding, delaying the decision of the first error can reduce early path loss and optimize SCLF performance.

[0033] By proposing an LLR threshold and comparing the magnitude of the LLR with the threshold, it is determined that, when N is sufficiently large, the magnitude of the LLR for any information bit must be greater than or equal to the threshold. Bits with an LLR amplitude below the LLR threshold are unreliable and typically correspond to the true first error location. Based on the definition of channel error probability, we can derive the following formula (6):

[0034] (6)

[0035] Using the monotonicity of the Q function, we can obtain equation (7):

[0036] (7)

[0037] The Q(x) function has the following when x is large: Therefore, we can obtain equation (8):

[0038] (8)

[0039] Bundle Substituting into equation (8), we obtain equation (9):

[0040] (9)

[0041] Through the above proof, we obtain inequality (10):

[0042] (10)

[0043] As the code length N increases, the absolute value of the LLR (Limited Range Ratio) of all information bits in the polar code becomes larger, indicating that its reliability improves accordingly. If the LLR amplitude of a certain information bit is lower than... (C is a constant coefficient), then it can be considered unreliable in an asymptotic sense. This theoretical limit provides guidance for the design of the threshold. At the same time, in order to ensure that the flip set can hit the first erroneous bit with a high probability under the condition of finite code length, based on a large number of Monte Carlo simulation results, an empirical threshold formula was obtained by curve fitting, as shown in Equation (5). This formula can dynamically adapt to the changes in code length N and maximum number of flip attempts T. The threshold filtering obtained by using the threshold formula has better decoding performance than taking fixed parameters.

[0044] (3) Combined with appendix Figure 3 4. Demonstrate the superiority of the method of the present invention through simulation as follows:

[0045] The CA-SCL decoding algorithm is the scheme proposed in the literature [1] “Niu Kai, Chen Kai. CRC-Aided Decoding of Polar Codes[J]. IEEE Communications Letters, 2012, 16(10): 1668-1671.”;

[0046] The CS-SCLF decoding algorithm is the scheme proposed in the literature [2] “YU YR, PAN ZW, LIU N, et al. Successive cancellation list bit-flip decoder for polar codes[C]. 2018 10th International Conference on Wireless Communications and Signal Processing(WCSP). Hangzhou: IEEE, 2018: 1-6.”

[0047] The DPost decoding algorithm is the scheme proposed in reference [3] "WANG ZX, PAN YH, LIN YH. Post-processing for CRC-aided successive cancellation list decoding of polar codes[J]. IEEE Communications Letters. 2020, 24(7): 1395-1399.";

[0048] The AS-SCLF decoding algorithm is the scheme proposed in the literature [4] "You W, Yuan J, Yu L, et al. An improved AS-SCLF decoding algorithm of polar codes based on the assigned set[J]. Optoelectronics Letters, 2022, 18(11): 694-698."

[0049] To verify the superiority of the method proposed in this invention, simulation analysis was performed on the simulation results to assess complexity and bit error rate performance. Figure 3 The error rate performance of the decoding method proposed in this invention and the CA-SCL method in reference [1], CS-SCLF method in reference [2], DPOST method in reference [3], AS-SCLF method in reference [4] are compared under the same simulation conditions. The simulation conditions are: code length N=1024, code rate The CRC length is 16 and the generator polynomial is... The polar code is transmitted via binary phase shift keying (BPSK) modulation over an additive white Gaussian noise (AWGN) channel. Figure 3 It can be seen that the decoding algorithm proposed in this paper has the best performance compared with other SCLF decoding algorithms, with a block error rate of [missing information]. At that time, compared with the CA-SCL decoding algorithm, the CS-SCLF decoding algorithm, the D-POST decoding algorithm, and the AS-SCLF decoding algorithm have a signal-to-noise ratio gain of approximately 0.24dB, 0.19dB, 0.1dB, and 0.08dB, respectively.

[0050] We use the average number of decoding operations to measure the computational complexity of decoding algorithms. The average number of decoding operations for each algorithm is as follows: Figure 4 As shown, in the low signal-to-noise ratio (SNR) region, i.e., under poor channel conditions, the proposed decoding algorithm reduces the average number of decoding operations by approximately 5%, 14%, and 17% compared to the AS-SCLF, D-POST, and CS-SCLF decoding algorithms, respectively, at an SNR of 1dB. At an SNR of 1.5dB, the Th-SCLF decoding algorithm reduces the average number of decoding operations by approximately 14% compared to the AS-SCLF algorithm, 17% compared to D-POST, and 20% compared to the CS-SCLF algorithm. With increasing SNR, the average number of decoding operations for all SCLF decoding algorithms shows a significant decreasing trend, and in the high SNR range, the number of decoding operations gradually converges to the level of the CA-SCL decoding algorithm.

[0051] Decoding methods with higher error performance and lower complexity are more advantageous. Therefore, the Th-SCLF decoding method proposed in this invention has strong advantages.

Claims

1. A polar code serial cancellation list bit-flipping (SCLF) decoding method based on the improvement of the Assigned Set (AS) and dynamic Logarithm Likelihood Ratio (LLR) threshold decision. This method addresses the problems of redundancy of flip candidate sets, inaccurate error location, high decoding delay and complexity caused by the reliance on static critical set (CS) or fixed channel reliability ranking in existing SCLF decoding algorithms. The method optimizes the flip candidate set through dual screening of AS set construction and dynamic LLR threshold decision, thereby improving decoding performance. The specific steps are as follows: Step 1: Construct the AS set. Based on the Cyclic Redundancy Check Aided Successive Cancellation List (CA-SCL) decoder with code length N, information length K, and list size L, calculate the path decision confidence of each information bit during the CA-SCL decoding process: First, define the total probability A(i) of the elimination path and the total probability B(i) of the retention path for the i-th bit, as shown in Equations (1) and (2), respectively: ； ； Equation (3) defines the path decision confidence of the i-th bit. The smaller the value, the smaller the metric difference between the retained path and the eliminated path, and the higher the probability of the decoder making an incorrect decision. According to the Gaussian approximation principle, Equation (4) defines the theoretical confidence threshold C(i). When the path decision confidence is lower than the theoretical confidence threshold, it is regarded as an element in the AS set. ； ； Step 2: Run the Successive Cancellation (SC) decoding to obtain the LLR sequence of the current received sequence. Based on the code length N and the maximum number of flips T, calculate the threshold by combining the threshold formula (5) of the code length N and the maximum number of flips. This threshold can dynamically adapt to the changes in the code length and the maximum number of flips, so as to achieve accurate screening of unreliable bits. ； Step 3: Perform a second filtering on the AS set, retaining only those that meet the requirements. bits (of which) (where LLR value is the value of the i-th bit), sort the filtered bits in ascending order of LLR value to obtain the optimized flipped CS set; Step 4: The improved SCLF decoding algorithm based on the AS set and dynamic LLR threshold decision performs CA-SCL decoding. If a path passes the Cyclic Redundancy Check (CRC), the path with the smallest path metric (PM) is output as the decoding result. If all paths fail the CRC check, bit-flipping re-decoding is performed based on the optimized flipped CS set. The specific rules are as follows: only nodes in the SC state of the decoding tree (i.e., nodes that retain only one path) are bit-flipped; nodes in the cloned state (both paths are retained) and the deleted state (both paths are eliminated) are not processed. Flipping re-decoding is performed sequentially according to the bit order in the optimized CS set. After each flip, the PM value is recalculated and the CRC check is performed. If a path that passes the CRC check is found within the maximum number of flips, the decoding result with the smallest PM value in that path is output. If the maximum number of flips is reached and the check still fails, the path with the smallest PM in the first CA-SCL decoding is output.

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