A low-complexity decoding method based on SC decoding

Abstract

This invention belongs to the field of channel coding technology, specifically relating to a low-complexity decoding method based on SC decoding. The method includes: performing SC decoding at the decoding end, followed by CRC verification; if the verification passes, the decoding result is obtained; otherwise, CA-SCL decoding is performed, including calculating a metric value based on the channel reliability estimate obtained after SC decoding, the log-likelihood ratio of the information bits, and the index value of the information bits; constructing a path splitting set B based on the metric value; performing path splitting on the path splitting set B, with the remaining bits directly hard-determined to obtain the decoding path; after decoding, performing CRC verification on all paths; if a path passes the CRC verification, selecting the path with the smallest PM value as the successfully decoded path; otherwise, decoding fails, and a retransmission of information is requested. This invention reduces the number of decoding path splits and the average list size, thus reducing decoding complexity.

Description

Technical Field

[0001] This invention belongs to the field of channel coding technology, specifically relating to a low-complexity decoding method based on SC decoding. Background Technology

[0002] Polar codes, as a novel channel coding method based on channel polarization, can achieve Shannon channel capacity on Binary Input Discrete Memoryless Symmetric Channels (BI-DMSCs) when the code length is sufficiently long, and possess a recursive encoding and decoding structure. Due to their superior error correction capabilities and lower encoding and decoding complexity, polar codes have been adopted by the 3rd Generation Partnership Project (3GPP) as the coding scheme for control channels in 5G Enhanced Mobile Broadband (eMBB) scenarios.

[0003] SC decoding is a suboptimal decoding algorithm, with unsatisfactory bit error rate performance under finite code lengths. To improve the BLER (Block Error Rate) performance of polar code decoding, researchers proposed a new CA-SCL decoding algorithm, but its complexity is high. To reduce its complexity, the AD-SCL decoding algorithm was further proposed. This algorithm starts with a list length L of 1, essentially performing SC decoding first, then checking if it passes the CRC check. If it fails the CRC check, the list length is increased to twice the original length, L←2L, until the CRC check succeeds. Compared to the CA-SCL decoding algorithm, where L starts with a large fixed value, simulations show that the AD-SCL decoding algorithm reduces complexity. However, the AD-SCL decoding algorithm may require multiple decoding operations, leading to an increased maximum decoding delay, and it does not fully utilize SC decoding information to reduce decoding complexity.

[0004] To reduce the path splitting complexity of CA-SCL, a post-decoding processing algorithm called PSS-SS-SCL (Path Splitting Selecting Strategy based on Search Set Successive Cancellation List) was proposed. This algorithm is characterized by performing path splitting only on information bits within a fixed Search Set (CS) set, while the remaining information bits undergo direct hard decision-making. Since the CS set contains over 90% of the error bits, its performance loss compared to the original CA-SCL is minimal, reducing the number of splits by 20%-50% and lowering the complexity of path splitting during decoding. However, because the CS set is fixed, there is a certain performance loss in decoding. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a low-complexity decoding method based on SC decoding, which includes:

[0006] S1: Perform SC decoding at the decoding end, and then perform CRC verification. If the verification passes, the decoding is correct and the decoding result is obtained; otherwise, proceed to steps S2 to S5.

[0007] S2: Calculate the metric value based on the channel reliability estimate obtained after SC decoding, the log-likelihood ratio of the information bits, and the index value of the information bits;

[0008] S3: Construct the path splitting set B based on the metric values;

[0009] S4: Perform CA-SCL decoding based on the path splitting set B to obtain L decoding paths;

[0010] S5: Perform CRC check on all paths. If a path passes the CRC check, select the path with the smallest PM value as the path to be successfully decoded; otherwise, decoding fails and a retransmission of information is requested.

[0011] Preferably, the formula for calculating the metric value is:

[0012]

[0013] Among them, M i LLR represents the metric value of the i-th information bit. i GLLR represents the log-likelihood ratio of the i-th information bit. i This represents the channel reliability estimate for the i-th information bit, and floor(·) indicates rounding down.

[0014] Preferably, the process of constructing the path split set includes:

[0015] The first three information bits of node R1 are used to form a TCS set;

[0016] Construct set A based on the TCS set;

[0017] Sort the information bits in set A in ascending order according to the metric value, and take the first T information bits to form a set path split set B.

[0018] Preferably, the process of constructing set A based on the TCS set includes:

[0019] Calculate the absolute value of the log-likelihood ratio (LLR) of each information bit in the TCS set. i |and the absolute error of the log-likelihood ratio and the channel reliability estimate|GLLR i -LLR i |;

[0020] Remove T1 of the largest |LLR values ​​from the TCS set. i |The information bits of the value are used to obtain set A1. The T1 smallest |GLLR values ​​are then removed from the TCS set. i -LLR i The information bits of the value are used to obtain set A2;

[0021] The intersection of sets A1 and A2 is the set A.

[0022] Preferably, the process of CA-SCL decoding of information bits according to the path split set B includes:

[0023] Determine whether the current information bit is an element in the path split set B. If it is, perform path splitting and decode using the traditional CA-SCL decoding method; otherwise, perform a hard decision directly on the current information bit.

[0024] Preferably, the formula for calculating PM values ​​is as follows:

[0025]

[0026] in, Information bit u i The path metric of the l-th path. Information bit u i-1 The path metric of the l-th path. Information bit u i The estimated value for the l-th path, Information bit u i In the LLR value of the l-th path, sign(·) is the sign function.

[0027] The beneficial effects of this invention are as follows: This invention designs a low-complexity decoding method based on SC decoding. Subsequent CA-SCL decoding is only performed when SC decoding fails. The method utilizes the LLR (log-likelihood ratio) after SC decoding to obtain a reliable estimate of the channel GLLR for Gaussian channel selection. i The metric M is composed of the index position i of the information bit. i And based on the metric M i The path split set for CA-SCL decoding changes continuously as decoding progresses. At high signal-to-noise ratios, SC decoding performs well, making a second CA-SCL decoding impractical. Performing an initial SC decoding further reduces decoding complexity and provides an LLR value for selecting the path split set A. The path split set B in this invention is smaller than the CS set in the PSS-SS-SCL algorithm, thus reducing the number of decoding path splits and the average list size. Furthermore, this invention decodes at most twice, resulting in lower latency compared to the traditional AD-SCL decoding algorithm. Attached Figure Description

[0028] Figure 1 This is a flowchart of the low-complexity decoding method based on SC decoding in this invention;

[0029] Figure 2 In this invention, the code length N = 2 4 A schematic diagram of the SC decoding tree at that time;

[0030] Figure 3 The simulation comparison graph shows the BLER performance of the present invention and the comparative method.

[0031] Figure 4 This is a simulation comparison chart of the average list length of the present invention and the comparative method. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] This invention proposes a low-complexity decoding method based on SC decoding (SC-SCL), such as... Figure 1 As shown, the method includes the following:

[0034] S1: Perform SC decoding at the decoding end, and then perform CRC verification. If the verification passes, the decoding is correct and the decoding result is obtained; otherwise, proceed to steps S2 to S5.

[0035] The polar code is sent to the decoder through the encoder. The decoder decodes it. First, it is decoded using traditional SC decoding. After decoding, a CRC check is performed. If the check passes, it means that the decoding is correct and the decoding result is obtained; otherwise, the following steps (S2 to S5) are executed.

[0036] S2: Calculate the metric value based on the channel reliability estimate obtained after SC decoding, the log-likelihood ratio of the information bits, and the index value of the information bits.

[0037] Based on the SC decoding results, the log-likelihood ratio (LLR) of each information bit can be obtained. i Channel reliability estimate GLLR i Specifically, |LLR i | is the log-likelihood ratio of information bit i obtained after the first SC decoding, GLLR i It can be done through formula get, Let Q(·) represent the error probability of the i-th bit, and let Q(·) be a monotonically decreasing function.

[0038]

[0039] GLLR is essentially a log-likelihood ratio, a standard used in Gaussian constructions to measure channel reliability. After channel polarization, the Gaussian approximation is used to rank the channel reliability, selecting the most reliable channel to transmit information bits and CRC bits, while the remaining channels transmit frozen bits, and the index value i of the information bits is obtained.

[0040] In some embodiments, if the polar code length is 1024, the information bit length is 520, the code rate is 1 / 2, and the CRC length is 8, then AWGN channel BPSK modulation is used. LLR i Take {LLR0,...,LLR} 519}, taking the absolute value of this LLR value yields {|LLR0|,...,|LLR} 519 In the context of LLR, LLR can be used as an indicator to measure the decoding error of a certain information bit. The higher the LLR, the lower the probability of error in that information bit.

[0041] To obtain a better path splitting set B, consider using a Gaussian construction method to select the channel {GLLR0,...,GLLR}. 519 The GLLR value is used as a metric; a higher GLLR value indicates a more reliable channel. i and LLR i We take the absolute value of the difference between the log-likelihood ratio and the channel reliability estimate, which is the absolute error, to obtain |GLLR|. i -LLRi |;If|LLR i | Same, | GLLR i -LLR i A large difference indicates that the information bit is affected by greater noise. Therefore, The smaller the value, the more information bits u i It is easier to include unreliable information in a collection.

[0042] Based on the polarization characteristics of polar codes, the SC and SCL decoding algorithms are a serial decoding process, meaning that the decoding result of the preceding information bits will affect the decoding result of the following information bits. Therefore, the index value of the information bits is also considered as a metric. Furthermore, based on the channel reliability estimate, the log-likelihood ratio of the information bits, and the index value of the information bits, a metric value M is obtained. i , represented as:

[0043]

[0044] Among them, M i This represents the metric value of the i-th information bit, and floor(·) represents rounding down.

[0045] S3: Construct the path splitting set B based on the metric values.

[0046] The first three information bits of node R1 are used to form the unreliable information set TCS, where node R1 is a single information bit or a series of consecutive information bits.

[0047] like Figure 2 As shown, taking a polar code with a code length of N=8 as an example, the CS set consists of the first information bit of node R1, and the elements included in the CS set are {u5, u7, u...} 10 ,u 12 To include more unreliable information bits, the CS set is expanded by selecting the first three bits of node R1 to form the TCS set, i.e., the TCS set contains the elements {u5, u7, u...}. 10 ,u 11 ,u 12 ,u 13 ,u 14}

[0048] Construct set A based on the TCS set, specifically including the following:

[0049] To make the metric M i Selecting unreliable information bits requires solving two problems:

[0050] Question 1: M i In A very small value could be caused by one of the following three situations:

[0051] (1) Case 1: |LLR i The value is very large, |GLLR i -LLR i The value of | is also very large, and the result can be large or small;

[0052] (2) Case 2: |LLR i The value is very small, |GLLR i -LLR i The value of | is also very small, and its result can be large or small;

[0053] (3) Case 3: |LLR i The value is very small, |GLLR i -LLR i When the value of | is large, the result is small.

[0054] Considering |LLR i The larger the value, the more reliable the corresponding information bits; |GLLR i -LLR i The smaller the value, the less the corresponding information bit is affected by noise. Therefore, to obtain the information bits, cases one and two are excluded. The value is small.

[0055] Question 2: |GLLR i -LLR i The value is very large, which may be caused by two situations.

[0056] (1) Case 1: |GLLR i |>|LLR i |;

[0057] (2) Case 2: |GLLR i |<|LLR i |

[0058] Scenario 2 | LLR i A large value indicates that the information bit u i The error rate is low, so scenario two does not meet the requirements and should be excluded from the second scenario.

[0059] In summary, the two problems to be solved are Case 3 of Problem 1 and Case 1 of Problem 2. The solution of this invention is: calculate the absolute value of the log-likelihood ratio |LLR| for each information bit in the TCS set. i |and the absolute error of the log-likelihood ratio and the channel reliability estimate|GLLR i -LLR i |;Remove T1 of the largest |LLR from the TCS set i|The information bits of the value are used to obtain set A1. The T1 smallest |GLLR values ​​are then removed from the TCS set. i -LLR i |The information bits of the value are used to obtain set A2; the intersection of sets A1 and A2 is used to obtain set A.

[0060] The above method excludes a portion of larger |LLRs i |Value information bits and a smaller portion|GLLR i -LLR i The information bits of the | value indicate that some cases of problem one and case two, as well as case two of problem two, have been excluded, thus solving the two problems mentioned above relatively well.

[0061] Calculate the metric value {M0,...,M} for each information bit in set A. length(A) Sort the information bits in set A in ascending order according to the metric value, and take the first T information bits to form a path splitting set B{M0,...,M T Set B is used for CA-SCL path splitting.

[0062] S4: Decode the information bits using CA-SCL based on the path splitting set B to obtain L decoding paths.

[0063] During CA-SCL decoding, it is determined whether the current information bit is an element in the path splitting set B. If so, path splitting is performed to obtain L decoding paths, where L is an exponent of 2. Otherwise, a hard decision is made on the current information bit based on its LLR value.

[0064] S5: Perform CRC check on all paths. If a path passes the CRC check, select the path with the smallest PM value as the successfully decoded path and obtain the decoding result of the current information bits; otherwise, the decoding fails and a retransmission of information is requested.

[0065] The formula for calculating PM values ​​is:

[0066]

[0067] in, Information bit u i The path metric of the l-th path. Information bit u i-1 The path metric of the l-th path. Information bits u representing the l-th path i The estimated value, Information bit u i The LLR value of the l-th path; sign(·) is the sign function, representing:

[0068]

[0069] Evaluation of the present invention:

[0070] Under the same simulation environment, namely code length N=1024, K=512, code rate R=1 / 2, CRC length of 8, L=8, the low-complexity decoding method SC-SCL proposed in this invention is simulated and analyzed with the traditional CA-SCL decoding method and the PSS-SS-SCL decoding method.

[0071] like Figure 3 As shown, the SC-SCL path splitting algorithm proposed in this invention exhibits very little performance loss compared to the traditional CA-SCL decoding. At high signal-to-noise ratios (SNR), it closely approximates or even surpasses the performance of the CA-SCL decoding algorithm. This is because at high SNR, the channel environment is better, resulting in more pronounced channel polarization. The reliable set selected using GLLR is more accurate, and direct hard decision-making on the reliable set reduces the propagation of erroneous paths, thus improving decoding performance. (BLER is 10...) -6 At that time, the SC-SCL path splitting algorithm was 0.5 dB better than AD-SCL decoding and 0.3 dB better than PSS-SS-SCL decoding, indicating that obtaining the path splitting set based on SC decoding information is relatively reliable. Figure 4 As shown, the average number of lists in the SC-SCL algorithm is significantly lower than that of the CA-SCL and PSS-SS-SCL decoding algorithms. At high signal-to-noise ratios, the AD-SCL algorithm has a slightly higher number of lists than the SC-SCL algorithm, but its BLER performance is worse and it also has higher latency. The path split numbers for the four algorithms are: CA-SCL 512, AD-SCL 512, PSS-SS-SCL 120, and SC-SCL 96. The SC-SCL algorithm has fewer path splits than the other three. This demonstrates that the algorithm proposed in this invention reduces the average number of lists and path splits while maintaining BLER performance, thus reducing decoding complexity.

[0072] While maintaining the same decoding performance, the decoding complexity and number of splits of this invention are reduced by more than 20%; and because this invention decodes at most twice, it has a lower latency compared to the traditional AD-SCL decoding algorithm.

[0073] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A low complexity decoding method based on SC decoding, characterized in that, include: S1: Perform SC decoding at the decoding end, and then perform CRC check. If the check passes, the decoding is correct and the decoding result is obtained. Otherwise, proceed to steps S2-S5; S2: Calculate the metric value based on the channel reliability estimate obtained after SC decoding, the log-likelihood ratio of the information bits, and the index value of the information bits; the formula for calculating the metric value is: ； wherein, represents a metric value of the i-th information bit, represents a log-likelihood ratio of the i-th information bit, represents a channel reliability estimation value of the i-th information bit, represents a floor function; S3: Construct the path split set B based on the metric values; the process of constructing the path split set includes: The first three information bits of node R1 are used to form a TCS set; Construct set A from the TCS set; the process of constructing set A from the TCS set includes: Computing the absolute value of the log-likelihood ratio of each information bit in the TCS set and the absolute error of the log-likelihood ratio and the channel reliability estimate ; removing from the set of TCSs information bits of the maximum value, resulting in a set removing from the set of TCSs information bits of the minimum value, resulting in a set ; For sets and Taking the intersection yields set A; Sort the information bits in set A in ascending order according to the metric value, and take the first T information bits to form a set path split set B; S4: Perform CA-SCL decoding based on the path splitting set B to obtain L decoding paths; the process of performing CA-SCL decoding on the information bits based on the path splitting set B includes: Determine whether the current information bit is an element in the path split set B. If it is, perform path splitting and decode using the traditional CA-SCL decoding method; otherwise, perform a hard decision directly on the current information bit. S5: Perform CRC check on all paths. If a path passes the CRC check, select the path with the smallest PM value as the path to be successfully decoded; otherwise, decoding fails and a retransmission of information is requested.

2. The low-complexity decoding method based on SC decoding according to claim 1, characterized in that, The formula for calculating PM values ​​is: ； in, Information bits The path metric of the l-th path. Information bits The path metric of the l-th path. Information bits The estimated value for the l-th path, Information bits The LLR value of the l-th path, It is a symbolic function.

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