A polar code SCLF decoding method based on an improved first key set

Abstract

The application particularly relates to a polar code SCLF decoding method based on an improved first key set, and belongs to the technical field of channel coding, which takes the first key set as an initial key set, then calculates a theoretical value of bit unreliability by using a channel error probability, calculates an actual value of the bit unreliability by using a path metric value obtained through CA-SCL decoding, compares the actual value of the bit unreliability with the theoretical value, identifies error bits containing SC state paths in the first key set, arranges the error bits in ascending order of channel reliability to form an improved first key set, and finally exchanges decision results on SC state paths in the improved first key set when the first CA-SCL decoding fails. Simulation results show that the method has better error performance and lower complexity compared with RCS-SCLF and D-Post-SCLF decoding methods, and can be combined with a small list CA-SCL decoder to achieve the performance of a large list CA-SCL decoder.

Description

Technical Field

[0001] This invention belongs to the field of channel coding technology and relates to a polar code successive cancellation list bit-flip based on the improved first critical set (IFCS-SCLF) decoding method. This method mainly constructs an improved first critical set from the decoded error bits, and then, when the first cyclic redundancy check-aided successive cancellation list (CA-SCL) decoding fails, swaps the decision results on the successive cancellation (SC) state paths within the improved first critical set. Background Technology

[0002] The scheme combining polar code channel coding and SC decoding, proposed by Professor Arikan, has been theoretically proven for the first time to achieve channel capacity in general discrete memoryless symmetric channels. Compared with traditional channel coding schemes, polar codes have lower encoding and decoding complexity and better error correction performance. Therefore, polar code encoding and decoding methods are currently a research hotspot, and polar codes have been successfully selected as the channel coding scheme for control channels in 5G (5th Generation mobile communication) enhanced mobile broadband (eMBB) scenarios, playing an important role in next-generation mobile communication systems.

[0003] However, due to its serial nature, SC decoding suffers from severe error propagation during the decoding process, resulting in poor performance under finite code lengths. To improve the performance of polar code SC decoding methods, researchers proposed the Successive Cancellation List (SCL) decoding method. SCL decoding improves error performance by retaining L optimal candidate paths during the decoding process. To further improve the SCL decoding method, researchers proposed the CA-SCL decoding method. This method adds a Cyclic Redundancy Check (CRC) code to verify the L paths generated at the end of SCL decoding. The path that passes the CRC check and has the lowest path metric (PM) value is used as the final decoding result. If no path passes the CRC check, the path with the lowest PM value is directly used as the final decoding result.

[0004] In the continuous improvement of polar code decoding algorithms, researchers proposed the Successive Cancellation Bit-Flip (SCF) decoding method. When SC decoding fails, re-decoding is performed, flipping one erroneous bit in each re-decoding process to prevent error propagation and thus improve error rate performance. Based on research on the SCF decoding method, researchers used distributed CRC codes to verify the SC decoding process. Once an SC decoding error is detected, the decoding process is immediately terminated, significantly reducing the complexity of the SCF decoding method. To further improve the error rate performance of the SCF decoding method, researchers used CRC codes and distributed parity check codes to detect and identify erroneous bits, making the location of the first erroneous bit caused by channel noise more accurate, thereby improving error rate performance. To further improve the SCF decoding method, researchers proposed the SCLF decoding method, which combines SCF decoding with CA-SCL decoding. If CA-SCL decoding does not produce an information sequence that passes the CRC code check, a re-decoding process is performed, exchanging the path competition results of the erroneous bits to correct them. Based on research on the SCLF decoding method, scholars have proposed a key set containing most error bits. Flipping bits in the key set can improve error rate performance. However, due to the influence of dynamic noise, the key set cannot accurately locate the first error bit. Therefore, scholars have proposed an advanced decision post-processing (D-Post) method. This method defines a new metric for finding error bits, calculates the confidence level of each bit using the PM value obtained during CA-SCL decoding, and flips bits according to their confidence levels from smallest to largest. To fully consider the impact of previous bit decoding on the current bit decoding, this invention proposes a polar code SCLF decoding method based on an improved first key set that can quickly and accurately locate the first decoding error bit. This method effectively suppresses the impact of error propagation during decoding, achieving better error rate performance and lower complexity. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a polar code SCLF decoding method based on an improved first key set. Using the first key set as the initial key set, decoding error bits are located by comparing the actual and theoretical values ​​of bit unreliability. These bits are then arranged in ascending order of channel reliability to form an improved first key set. When the initial CA-SCL decoding fails, re-decoding is performed. During each re-decoding process, one information bit in the improved first key set is flipped. By flipping the error bit, the decoding process is corrected, effectively reducing error propagation and thus improving error performance. Compared with the traditional SCLF decoding method, the complexity is significantly reduced.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] First, a First Critical Set (FCS) is constructed based on the partial order relationship of the polarization channels. The FCS consists of the first bit of each sub-polarization with a code rate of 1 (corresponding to the worst polarization channel among the sub-polarizations with a code rate of 1). The FCS is used as the initial critical set. Since the bit decoding paths in set A′ are all in a cloned state, they are always retained during decoding. and There are two possible outcomes, so flipping the bits in A′ is meaningless. We need to remove the bits in A′ in FCS to obtain the corrected first key set suitable for SCLF.

[0008] Then, the unreliability γ of the bit during the actual decoding process is calculated using the PM value generated by CA-SCL decoding. (i) The polarized channel is approximated as a binary-input additive white Gaussian noise (AWGN) channel. Assuming the transmitter uses all-zero codewords, the mean log-likelihood ratio (LLR) of the polarized channel is numerically calculated. The channel reliability is then determined based on the mean LLR; a higher mean indicates a more reliable channel. The channel error probability is calculated using the Gaussian approximation. use Calculate the theoretical value of bit unreliability. if This indicates that the decoding error rate of this bit is high, which can be used to optimize the corrected first key set. Because... It was derived using Gaussian approximation with an SC decoder, therefore, it is necessary to remove those that do not satisfy the formula from the modified first key set. In addition to the bits that do not contain SC state paths, the remaining bits are arranged in ascending order of channel reliability to form the improved first key set.

[0009] Finally, CA-SCL decoding is performed. If CA-SCL decoding is successful, the correct decoding path is output; otherwise, decoding is re-encoded. Each re-decoding process involves sequentially flipping and improving one bit in the first key set. If a path that passes CRC check is found during re-decoding, the decoding result of this path is output; otherwise, the next re-decoding process is performed. If no path that passes CRC check is found after reaching the maximum number of re-decoding attempts, the path with the smallest PM value in the initial CA-SCL decoding is output, thus achieving IFCS-SCLF decoding.

[0010] The beneficial effects of this invention are as follows:

[0011] The method of this invention can quickly and accurately locate the first decoding error bit, effectively suppress the impact of error propagation during the decoding process, improve the error performance of the SCLF decoding method, and greatly reduce the decoding complexity. Simulation results show that the IFCS proposed in this invention can more accurately identify the first error bit caused by channel noise than the RCS in reference [1] "YU Yongrun, PAN Zhiwen, LIU Nan, 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." Compared to the D-Post-SCLF decoding method in reference [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 key set proposed by the IFCS-SCLF decoding method can effectively reduce unnecessary re-decoding processes, obtain better error performance and lower complexity. The CA-SCL decoding method with a list size of L=32 has almost the same error performance in the low-to-medium signal-to-noise ratio region, and requires fewer re-decoding operations. Therefore, the decoding method proposed in this invention can be combined with a small-list CA-SCL decoder to achieve the expected performance of a large-list CA-SCL decoder. Attached Figure Description

[0012] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0013] Figure 1 This is a technical roadmap of the method of the present invention;

[0014] Figure 2 A schematic diagram of FCS;

[0015] Figure 3 Schematic diagram of CA-SCL and SCLF decoding trees;

[0016] Figure 4 Block error rate curves for the IFCS-SCLF decoding method under different α values;

[0017] Figure 5 Block error rate curves for different decoding methods;

[0018] Figure 6 A graph showing the average number of decoding operations for different decoding methods; Detailed Implementation

[0019] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0020] (1) Combined with appendix Figure 1 The specific implementation process of a polar code SCLF decoding method based on an improved first key set is as follows:

[0021] Step 1: Construct the FCS based on the partial order relationship of the polarization channel. The FCS consists of the first bit of each sub-polarization with a code rate of 1 (corresponding to the worst polarization channel among the sub-polarizations with a code rate of 1). For the CA-SCL decoder, the information bit index set is A. In the decoding u... i If the path metric matrix is ​​sorted, and If both decoding sub-paths are preserved, the path is said to be in a cloned state; if the path metric matrix is ​​sorted, and If both decoding sub-paths are deleted, the path is said to be in a deleted state; if, after sorting the path metric matrix, only [the path is retained], then [the path is considered deleted]. and One of the decoding paths is said to be in the SC state.

[0022] The first log2 L information bits are grouped into a set A′. The decoding paths of the bits in set A′ are all in a cloned state, and are always retained during decoding. and There are two possible outcomes, so flipping the bits in A′ is meaningless. We need to remove the bits in A′ from the FCS to obtain the Revised First Critical Set (RFCS) suitable for SCLF, which can be represented as RFCS = FCS\A′.

[0023] Step 2: For i∈RFCS, for each decoding path It will be expanded to and There are two paths, resulting in a total of 2L decoding paths. The L paths with the smallest PM values ​​are selected as the optimal candidate paths, forming a set. The unreliability of bits in actual decoding is defined as follows: and The probability of this is denoted as γ. (i)(i∈A\A′), γ (i) The larger the bit size, the less reliable the decoding; γ (i) The calculation is shown in formula (1).

[0024]

[0025] Will Let it be P c (i) Through P c (i) Equation (1) is simplified to Equation (2).

[0026]

[0027] Since the decoder cannot obtain the correct decoding sequence information, P is... c (i) Approximately Indicates that the received sequence is and If L optimal paths are retained The probability of.

[0028] use Let be the path metric for 2L paths. Without loss of generality, assume... The sizes of the paths are increasing, so the size of the path in the l-th path is... The probability of no decoding error is approximately: Since L paths with the smallest path metric values ​​are always retained in CA-SCL decoding, the total probability of retaining L paths is: The total probability of L deletion paths is: P c (i) It can be calculated using formula (3).

[0029]

[0030] Introduction P c (i) It can be rewritten as formula (4).

[0031]

[0032] Where α (0 < α < 1) is the compensation P c (i) The approximation factor α used is too large or too small, which will cause the approximate value to deviate from the actual value. Therefore, the value of α needs to be appropriate.

[0033] Step 3: Approximate the polarized channel as a binary input AWGN channel. Assuming the transmitter uses all-zero codewords, calculate the mean LLR of the polarized channel numerically, and then determine the channel reliability based on the mean LLR; a higher mean indicates a more reliable channel. The channel polarization pattern is derived from the structural characteristics of the polarized code. Polarization Channel and The LLR values ​​are all Gaussian random variables with variances twice their mean. Assume the channel... The mean LLR is Then the channel mean LLR The calculation is shown in formulas (5) and (6).

[0034]

[0035]

[0036] in

[0037]

[0038] The channel error probability is calculated as shown in formula (8).

[0039]

[0040] in erfc(x) is the complementary error function.

[0041] Step 4: Theoretically, the unreliability of a bit is defined as the situation where the previous bits were decoded correctly but u... i The probability of a decoding error is denoted as . Polarization channel error probability obtained using Gaussian approximation method To calculate The calculation is shown in formula (9).

[0042]

[0043] When bit u i When the unreliability in actual decoding is higher than the theoretical value, it means that the error rate of the bit is high during decoding. Therefore, RFCS can be optimized by equation (10).

[0044]

[0045] The optimized key set is represented as OFCS, which is expressed by formula (11).

[0046]

[0047] because It is derived by Gaussian approximation under the SC decoder. Therefore, it is necessary to remove bits that do not contain SC state paths in OFCS to ensure that all bits in the Improved First Critical Set (IFCS) contain SC state paths. Let κ represent the set of bits in OFCS that do not contain SC state paths. IFCS is represented by Equation (12).

[0048] IFCS=OFCS\κ (24)

[0049] Unlike the bit flipping order which is sorted by confidence level, this invention selects to sort the bits in the IFCS according to the order obtained by the Gaussian approximation method. The results are sorted in ascending order. The final IFCS will be used in the SCLF decoding method for polar codes based on the improved first key set in this invention.

[0050] Step 5: Perform CA-SCL decoding. If the initial CA-SCL decoding passes the CRC check, output the path with the smallest PM value that passes the CRC check. Otherwise, perform re-decoding based on IFCS. The re-decoding process sequentially flips the bits in the IFCS, flipping only one bit at a time. If the re-decoding process passes the CRC check, output the correct decoding path; otherwise, proceed to the next re-decoding process. When the number of re-decoding attempts reaches the maximum value without obtaining the correct decoding sequence, output the decoding path with the smallest PM value from the initial CA-SCL decoding.

[0051] For SCLF decoders, there are currently two bit-flipping schemes: the first is to flip the bit u. i The corresponding result of all decoding path contention decisions is the opposite of that of standard CA-SCL decoding. This flipping scheme can effectively avoid producing the same codeword estimate as standard CA-SCL decoding. The second method is to flip bit u. i The path contention decision results for the corresponding cloned state path and deleted state path remain unchanged, while the path contention decision result for the SC state path is the opposite of that in standard CA-SCL decoding. This is because the present invention... It is derived by Gaussian approximation under the SC decoder, therefore the second flipping scheme is selected for flipped bits.

[0052] (2) Combined with the appendix Figure 2 Explanation of the construction method of FCS:

[0053] FCS consists of the first bit of each 1-rate node (corresponding to the worst polarization channel among the sub-polarization codes with a 1-rate code). Figure 2The diagram shows a polar code with code length N = 8 and A = {4, 6, 7, 8}. Black nodes indicate that all leaf nodes are information bits, white nodes indicate that all leaf nodes are frozen bits, and gray nodes indicate that leaf nodes contain both information bits and frozen bits. Solid rectangles represent sub-polar codes with a code rate of 1. The bit indices in dashed rectangles constitute the FCS, represented as FCS = {4, 6, 7}.

[0054] (3) Combined with appendix Figure 3 The selection of the bit-flipping scheme is explained below:

[0055] According to the decoding u i Based on the state of the path, the flipping scheme is divided into two types. Assume the list size L = 4, u1, u2, u3, and u5 are information bits, u4 is a frozen bit, and u5 is the flipping bit. Black nodes represent retained paths, and white nodes represent deleted paths. Figure (a) shows the standard CA-SCL decoding process: node A's two extended paths are deleted and it is in the deleted state; node B's two extended paths are retained and it is in the cloned state; nodes C and D each retain only one extended path and are in the SC state. Figures (b) and (c) show two flipping schemes for the SCLF decoding method. In the flipping scheme shown in Figure (b), when decoding u5, the path competition decision results of all nodes are opposite to those in Figure (a), avoiding obtaining the same codeword estimate as standard CA-SCL decoding. In the flipping scheme shown in Figure (c), nodes A and B maintain the decision results of Figure (a), while nodes C and D have the opposite decision results. Since the key set constructed in this invention is related to SC decoding, (c) in the figure is selected as the flipping scheme of the method proposed in this invention.

[0056] (4) Combined with the appendix Figure 4 The optimal α value for the method of this invention is explained as follows:

[0057] The optimal α value can be obtained by simulating the error performance of the IFCS-SCLF decoder under different α conditions. Since the value of α needs to be moderate, α = 0.4, 0.5, 0.6, and 1 (without adding parameters) are selected for simulation analysis, and the maximum number of flips T = 50 is set. Figure 4 The results show that the decoder performance is poor when α = 1 (without adding a parameter), therefore adding the parameter α to formula (4) is feasible and necessary. (Comparison) Figure 4 The error rate performance of the decoder was analyzed when α = 0.4, 0.5, and 0.6, and it was found that the performance was best when α = 0.5.

[0058] (5) Combined with appendix Figure 5 Section 6 illustrates the superiority of the method of the present invention, and the simulation results are as follows:

[0059] To verify the superiority of the proposed method, an error performance and complexity simulation analysis was performed on the IFCS-SCLF decoder. The simulation conditions were: polar code length N = 1024, code rate R = 0.5, list size L = 8, codewords were BPSK modulated and transmitted over an AWGN channel, a Gaussian approximation construction method with a signal-to-noise ratio (SNR) of 2.5 dB was used, and the CRC checksum code length r = 16, with a corresponding generator polynomial g. 16 (x)=x 16 +x 15 +x 2 +1. The simulation iteration count is 10. 7 .

[0060] The IFCS-SCLF decoding method proposed in this invention is compared with the CA-SCL decoding method in reference [3] "NIU Kai, CHEN Kai. CRC-aided decoding of polar codes[J]. IEEE Communications Letters, 2012, 16(10): 1668-1671.", the RCS-SCLF decoding method in reference [1], and the D-Post-SCLF decoding method in reference [2], and the error rate and average number of decoding operations of the above methods are analyzed.

[0061] When the maximum number of flips T = 10, the IFCS-SCLF decoding method proposed in this invention exhibits the best error performance compared to the RCS-SCLF and D-Post-SCLF decoding methods. At T = 50 and a block error rate of 10... -4 At that time, the IFCS-SCLF decoding method has gains of approximately 0.2dB, 0.1dB, 0.29dB, and 0.12dB compared to the RCS-SCLF decoding method, the D-Post-SCLF decoding method, and the CA-SCL decoding method with list sizes of L=8 and 16, respectively. Moreover, it has almost the same bit error rate performance as the CA-SCL decoding method with a list size of L=32 in the low to medium signal-to-noise ratio region.

[0062] The computational complexity of the bit-flipping method can be described as the average number of decoding operations; a higher average number of decoding operations indicates higher computational complexity. At T = 10 and 50, the IFCS-SCLF decoding method proposed in this invention has the lowest complexity compared to the RCS-SCLF and D-Post-SCLF decoding methods. At T = 50 and a signal-to-noise ratio of 1dB, the complexity of the IFCS-SCLF decoding method is reduced by approximately 26% and 12% compared to the RCS-SCLF and D-Post-SCLF decoding methods, respectively. Normalizing the computational complexity of the CA-SCL decoding methods with list sizes L = 8, 16, and 32 to 1, 2, and 4, respectively, represents the equivalent number of decoding operations required for CA-SCL decoding. When the block error rate is less than 10... -3 In the region, the complexity of the IFCS-SCLF decoding method proposed in this paper is lower than that of the CA-SCL decoding method with list size L=16 and 32, which shows that the combination of the IFCS-SCLF decoding method and the small list CA-SCL decoder can achieve the performance of the large list CA-SCL decoder.

[0063] Decoding methods with higher error performance and lower complexity are more advantageous. Therefore, the IFCS-SCLF decoding method proposed in this invention has strong advantages.

Claims

1. A polar code successive cancellation list bit-flip (IFCS-SCLF) decoding method based on the improved first critical set. This method addresses the problem that current polar code successive cancellation list bit-flip (SCLF) decoding methods do not fully consider the impact of previous bit decoding on the current bit decoding. First, the first critical set is used as the initial critical set. Then, the channel error probability obtained by Gaussian approximation is used to calculate the theoretical value of bit unreliability. The actual value of bit unreliability is calculated using the path metric (PM) obtained by the Cyclic Redundancy Check Aided Successive Cancellation List (CA-SCL) decoding method. If the actual value of bit unreliability is greater than the theoretical value, it indicates that the decoding error rate of that bit is high. This is used to identify whether the first critical set contains successive cancellation (IFCS-SCLF) bit-flip. The erroneous bits of the SC state path are sorted in ascending order of channel reliability to form the Improved First Critical Set (IFCS). Finally, when the first CA-SCL decoding fails, the decision results on the SC state path in the IFCS are swapped, and the remaining bits are still decoded using the traditional Successive Cancellation List (SCL). This method specifically includes the following steps: Step 1: Construct the First Critical Set (FCS) based on the partial order relationship of the polarization channels. The FCS consists of the first bit of each sub-polar code with a code rate of 1 (corresponding to the worst polarization channel among the sub-polar codes with a code rate of 1). For the CA-SCL decoder, the information bit index set is... In decoding If the path metric matrix is ​​sorted, and If both decoding sub-paths are preserved, the path is said to be in a cloned state; if the path metric matrix is ​​sorted, and If both decoding sub-paths are deleted, the path is said to be in a deleted state; if, after sorting the path metric matrix, only [the path is deleted]... and If one of the decoding paths is in the SC state, then that path is said to be in the SC state. Before A set of information bits ,gather The bit decoding paths in the code are all in a cloned state, and are always retained during decoding. and Two possible outcomes, therefore for Flipping the bits in the FCS is meaningless and needs to be removed. The bits in the SCLF are used to obtain the Revised First Critical Set (RFCS), which is represented as follows: ; Step Two: For Each decoding path It will be expanded to and There are two paths, resulting in a total of 2L decoding paths. The L paths with the smallest PM values ​​are selected as the optimal candidate paths and form a set. The unreliability of bits in actual decoding is defined as... and The probability of is denoted as , The larger the bit size, the less reliable the decoding. The calculation is shown in formula (1): Will Recorded as ,pass Equation (1) is simplified to Equation (2): Since the decoder cannot directly obtain the correct decoding sequence information, therefore... Approximately Indicates that in the received sequence is and If L optimal paths are retained The probability of; use To represent the path metric for 2L paths, without loss of generality, assume The sizes of are in an increasing relationship, then the ... Path The probability of no decoding error is approximately: Since L paths with the smallest path metric values ​​are always retained in CA-SCL decoding, the total probability of retaining L paths is: The total probability of L deletion paths is Therefore Calculate using formula (3): Introduction ,Will Rewritten as formula (4): in To compensate The approximation factor used Values ​​that are too large or too small will cause the approximate value to deviate from the actual value. The value should be appropriate; Step 3: Approximate the polarization channel as a binary input additive white Gaussian noise (AWGN) channel. Assuming the transmitter uses all-zero codewords, calculate the mean logarithm likelihood ratio (LLR) of the polarization channel numerically. Then, determine the channel reliability based on the mean LLR; a higher mean indicates a more reliable channel. The channel polarization pattern is then derived from the structural characteristics of the polarization code. Polarization channel , and The LLRs are all Gaussian random variables with variances twice their mean, assuming the channel... The mean LLR is Then the channel , mean LLR , The calculation is shown in formulas (5) and (6): in Channel error probability The calculation is shown in formula (8): in , For complementary error functions, ; Step 4: Theoretically, the unreliability of a bit is defined as the previous bit decoding being correct but... The probability of a decoding error is denoted as . Polarization channel error probability obtained using Gaussian approximation method To calculate The calculation is shown in formula (9): When bits When the unreliability in actual decoding is higher than the theoretical value, it indicates that the error rate of this bit is high during decoding. Therefore, RFCS is optimized using formula (10): The optimized key set is represented by OFCS, which is expressed by formula (11): because This is derived using a Gaussian approximation within the SC decoder. Therefore, bits that do not contain the SC state path need to be removed from the OFCS to ensure that all bits in the IFCS contain the SC state path. The set of bits in OFCS that does not contain SC state paths is represented by formula (12): Unlike the typical SCLF decoding method that flips bits in ascending confidence order, this decoding method selects to flip the bits in the IFCS according to the Gaussian approximation method. The IFCS is sorted in ascending order and then applied to the SCLF decoding method of polar codes based on the improved first key set. Step 5: Perform CA-SCL decoding. If the first CA-SCL decoding passes the Cyclic Redundancy Check (CRC), the path with the smallest PM value that passes the CRC check is directly output. Otherwise, perform re-decoding based on IFCS. The re-decoding process sequentially flips the bits in the IFCS, flipping only one bit each time. If the re-decoding process passes the CRC check, the correct decoding path is output. Otherwise, the next re-decoding process is performed. When the number of re-decoding attempts reaches the maximum value and the correct decoding sequence is still not obtained, the decoding path with the smallest PM value in the first CA-SCL decoding is output. For SCLF decoders, there are currently two bit-flipping schemes: the first is to flip the bits. The corresponding result of all decoding path contention decisions is the opposite of that of standard CA-SCL decoding. This flipping scheme can effectively avoid producing the same codeword estimate as standard CA-SCL decoding; the second is bit flipping. The path contention decision results for the corresponding cloned state path and deleted state path remain unchanged. The path contention decision result for the SC state path is the opposite of that in standard CA-SCL decoding. This is because the decoding method of this method... It is derived by Gaussian approximation under the SC decoder, therefore the second flipping scheme is selected for the flipped bits.

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