A key set based polar code simplified SCL decoding method

Abstract

The application particularly relates to a key set-based simplified SCL decoding method of a polar code, and belongs to the technical field of channel coding.The method is characterized in that: firstly, according to the channel characteristics of the polar code, the minimum Hamming weight (MHW) of information bits and channel reliability are comprehensively considered to construct a key set; then, in actual decoding, the information bits in the key set still perform SCL decoding and path splitting, and the information bits outside the key set directly perform hard decision.Simulation results show that, compared with the traditional SCL decoding, the complexity of the proposed CS-SCL decoding method is reduced by at least 70%, and the computational complexity is also reduced compared with the PS-SS-SCL decoding method; and the error correction performance loss of the proposed CS-SCL decoding method is very small, which provides a good trade-off between the error correction performance and complexity of the polar code decoding method.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of channel coding, and relates to a polar code decoding method based on critical sets in channel coding. The method mainly combines the principle of a path reduction method based on critical sets and a successive cancellation list (SCL) decoding method of polar codes to provide a good trade-off between decoding performance and complexity for polar code decoding methods. BACKGROUND

[0002] Polar codes proposed by Arikan are the first type of code that can be proved to achieve the channel capacity of symmetric binary-input memoryless channels with binary input, and have been successfully selected as the coding scheme of control channels in the enhanced mobile broadband (eMBB) scenario of 5G standards. Polar codes are an important technology for new generation mobile communication systems. However, in the case of limited code length, channel polarization is not complete, and the performance of the actual SC decoding method is not ideal. Therefore, some scholars have proposed a successive cancellation list (SCL) decoding method that can preserve multiple decoding paths to improve performance. Although the SCL decoder has a performance close to that of the maximum likelihood (ML) decoder at high signal-to-noise ratios (SNRs), the decoding complexity of the SCL decoder increases to O(LNlogN) due to the copying, sorting, and deleting operations, making it difficult to be practically applied when the list size L is very large. To further improve the decoding performance, a cyclic redundancy check (CRC) aided SCL (CA-SCL) decoding method was proposed, which can save more memory space and delay time. Some scholars have proposed a successive cancellation stack (SCS) decoder, which uses a depth-first search method and has lower computational complexity than the SCL decoder, especially at high SNRs, where the complexity is close to that of the SC decoder. However, the storage complexity of the SCS decoder is higher than that of the SCL decoder to achieve the same decoding performance.

[0003] Because the SCL decoder splits each information bit when decoding, retaining both "0" and "1" results, each decoding path is split into two paths. The optimal decoding path remains at L until the decoding is completed, resulting in an increase in O(LNlogN) complexity. To reduce computational complexity, the number of unnecessary path splits can be reduced. Common methods include the key set method, the check code method, and the LLR threshold method. Some scholars have proposed a method to reduce path splitting. This method constructs a key set based on information bits with low reliability and only performs path splitting on information bits within the key set. In addition, some scholars have used the Gaussian approximation method to construct polar codes, using the first information bit of the code rate 1 node (or the first and second information bits when L is larger) to construct the key set. However, this results in a significant loss in error correction performance under the polarization weight (PW) channel reliability estimation method in the 5G standard. However, both methods only consider the reliability of the polarized channel, ignoring the impact of information bits with minimum Hamming Weight (MHW) on decoding errors. Therefore, the present invention comprehensively considers both and calculates channel reliability using the polarization weight method. This paper proposes a simplified polar code SCL decoding method based on key sets, which has low complexity and minimal decoding loss. Summary of the Invention

[0004] In light of this, the present invention aims to provide a simplified SCL decoding method for polar codes based on a key set. This method first constructs a key set based on the channel characteristics of the polar code, taking into account the minimum Hamming weight (MHW) of the information bits and channel reliability. Information bits within the key set still undergo SCL decoding, performing path splitting, while information bits outside the key set undergo direct hard decision making.

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

[0006] First, the polar code length N, the number of information bits m, and the number of cyclic redundancy check (CRC) bits r to be designed are selected. The reliability measurement parameter of each split channel is calculated using the polarization weight method. All split channels are sorted from high to low according to channel reliability to obtain the sorted split channel position index value sequence w1. N , and select the first m+r with the largest reliability, which is w1 N The split channels corresponding to the first m+r index values ​​are used as the non-frozen bit set A, and the remaining Nmr split channels are used as the frozen bit set A (usually set to 0). c .

[0007] Then for sequence u1 mPerform CRC encoding and polar code encoding, and convert sequence u1 m+r As a non-frozen bit, it is input into the polar code encoder for polar code encoding to obtain the polar code encoded codeword x1 N , and then x1 N Incoming channel for transmission.

[0008] The polar code is then decomposed into six sub-polar codes. The index of each sub-polar code containing a MHW bit is included in the key set. If the number of bits with MHW in a sub-polar code is less than 1% (rounded up) of the number of elements in the non-frozen bit set, the index of the sub-polar code containing a lower MHW bit is also included in the key set. The polarization weight method is used to calculate the polarization weight of each channel, thereby sorting the channels in ascending order of reliability. Using the variable a, the indices of channels with the lowest polarization weight among the a% of non-frozen bits are added to the key set. The value a can be flexibly selected based on the target block error rate. If high error correction performance is required, the channels with the lowest percentage of low PW values ​​are included in the key set, provided that the block error rate is barely reduced (compared to the original SCL decoding method without path reduction). If low error correction performance is required, the channels with the a% of low PW values ​​are included in the key set based on the target block error rate.

[0009] Finally, the corresponding decoding method is used at the receiving end. Information bits within the key set still undergo SCL decoding, resulting in path splitting; information bits outside the key set undergo direct hard decision. The path metric (PM) value is updated based on the LLR at this point. After decoding, the path with the lowest PM is selected from the paths that pass the CRC check as the decoder output. In the same simulation environment, the proposed simplified SCL decoding method for polar codes based on key sets was simulated and compared with other similar decoding methods.

[0010] The beneficial effects of the present invention are:

[0011] A simplified SCL decoding method for polar codes based on key sets is proposed. This method first constructs a key set based on the channel characteristics of polar codes, taking into account the minimum Hamming weight (MHW) of the information bits and the channel reliability. Information bits within the key set still undergo SCL decoding and path splitting, while information bits outside the key set undergo direct hard decisions. This method has the following advantages: 1. It reduces the number of path sorting, duplication, and deletions during decoding, further reducing the computational complexity of SCL decoding. 2. The parameter a introduced to control low-reliability channels can be flexibly selected, facilitating achieving a target block error rate (BLER) while reducing complexity to ensure decoding performance. Simulation experiments show that the proposed CS-SCL decoding method reduces the decoding complexity by at least 70% compared to the traditional SCL method, and also reduces the decoding complexity compared to the simplified SCL (PS-SS-SCL) decoding method, which constructs the key set based on the first two information bits of a rate 1 node. Furthermore, the proposed CS-SCL decoding method exhibits minimal loss in error correction performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

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

[0014] Figure 2 Schematic diagram of the SCL decoding path for the polar code path reduction method;

[0015] Figure 3 This is a comparison chart of the block error rate performance of four polar code decoding methods when the code length N = 1024;

[0016] Figure 4 The block error rate performance comparison chart of four polar code decoding methods when the code length N=512. 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 attachment Figure 1 The specific implementation method of a simplified SCL decoding method for polar codes based on a key set is as follows:

[0019] In the polar code encoding stage, the code length N of the polar code to be designed, the number of information bits m, and the number of cyclic redundancy check bits r are first selected. The reliability measurement parameter of each split channel is calculated using the polarization weight method. All split channels are sorted from high to low according to channel reliability to obtain the sorted split channel position index value sequence. And select the first m+r with the highest reliability, that is The split channels corresponding to the first m+r index values ​​are used as the non-frozen bit set A, and the remaining Nmr split channels are used as the frozen bit set A (usually set to 0). c .

[0020] Then the sequence Perform CRC encoding and polar code encoding to convert the sequence As a non-frozen bit, it is input into the polar code encoder for polar code encoding to obtain the polar code encoded codeword

[0021] The polar code is decomposed into 6 sub-polar codes, and the code length of the first and last sub-polar codes is N = 2 n -2 , corresponding to the smallest and largest parts of the bit index respectively, and the code length of the remaining four sub-polar codes is N = 2 n-3 , located between two longer sub-polarization codes. The index value of the MHW bit in each sub-polarization code shown in formula (1) is included in the key set. If the number of bits with MHW in the sub-polarization code is less than 1% (rounded off) of the number of elements in the non-frozen bit set, the index of the sub-MHW bit in the sub-polarization code shown in formula (2) is also included in the key set. i Represents the set of information bits between the i-1th PC bit and the i-th PC bit.

[0022]

[0023]

[0024] Among them, the generator matrix G N The Hamming weight value of the i-th row in is the number of elements 1. d in formulas (1) and (2) m and d s They represent the MHW and sub-MHW of the non-frozen bit set respectively.

[0025] The polarization weight method is used to calculate the polarization weight value of each channel according to formula (3), so as to sort the reliability of the channels from small to large.

[0026]

[0027] Referring to variable a, after adding low-Hamming-weight channels to the key set, we continue to add a% of channels with low PW values. a can be flexibly selected based on the target block error rate. If the error correction performance requirement is high, then with little reduction in the block error rate (compared to the original SCL decoding method without path reduction), we select the channels with the minimum percentage of low PW values ​​to add to the key set (for example, when the code length N = 1024, we select a = 20). This reduces the computational complexity of SCL decoding, and the complexity reduction is relatively small. Conversely, if the error correction performance requirement is low, we select a% of channels with low PW values ​​to add to the key set based on the target block error rate (for example, when the code length N = 1024, we select a = 15). This reduces the computational complexity significantly, but with a significant loss in error correction performance.

[0028] At the receiving end, the value of the received signal is first converted into a logarithm likelihood ratio (LLR), as shown in formula (4):

[0029]

[0030] In formula (4), y i represents the received signal value of each bit, σ 2 represents the variance of the channel noise. Then each path obtains the decision LLR of each bit by performing the corresponding f and g operations.

[0031] L≈sign(L1)sign(L2)min{|L1||L2|} (5)

[0032] L=(1-2U1)L1+L2 (6)

[0033] Formula (5) represents the f operation which is easy to implement in hardware, and formula (6) represents the g operation, where L represents the LLR output by the operation, L1 and L2 represent the LLR input to the operation, and U1 represents the decoded estimated value of the previous bit input to the operation.

[0034] When decoding information bits in the key set, SCL decoding is still performed and path splitting is performed. Information bits outside the key set are directly hard-determined as shown in formula (7).

[0035]

[0036] The PM is updated according to the LLR at this time as shown in formula (8). When the decoder decodes other positions, SCL decoding is performed. After the decoding is completed, the path with the smallest PM is selected from the paths that pass the CRC check as the output result of the decoder.

[0037]

[0038] in u represents the path metric value of the lth decoding path after decoding the ith bit, i,l u represents the decoding estimate value of the ith bit in the lth decoding path, u represents the LLR of the decoding decision of the ith bit in the lth decoding path.

[0039] (2) Combined with the Figure 2 The polarization code is based on the key set to realize the path reduction principle:

[0040] If the channel where the non-frozen bit is located is reliable enough, even if only one of the "0" or "1" decoding results is retained through formula (7), the SCL decoder still retains the original L paths without splitting to produce 2L paths, which reduces the number of candidate paths and does not significantly reduce the error correction performance of the polarization code. Therefore, the L SC decoders only need to update their decoding results, without selecting L paths with smaller PM values from 2L candidate paths, avoiding the duplication, sorting and deletion of paths in the selection process, thereby reducing the computational complexity of decoding. For example, if u1 to u4 are information bits, the channels where u1 and u2 are located are unreliable channels, and the channels where u3 and u4 are located are reliable channels, and the list L is equal to 4, in the decoding process, the SCL decoder saves two decoding results of u1 and u2, and saves one decoding result of u3 and u4. Since the decoding results of u1 and u2 saved by each SC decoder are different, the estimate values of u3 and u4 in the decoding process are also different; in the decoding of u1 and u4, L candidate paths are reduced, and the process of path duplication, sorting and deletion is reduced by 1 time, thereby reducing the computational complexity of SCL decoding.

[0041] (3) Combined with the Figure 3 The superiority of the proposed decoding method is demonstrated as follows:

[0042] The PS-SS-SCL(1) decoding method and the PS-SS-SCL(2) decoding method are the schemes proposed in the literature [1]“Gao Chenyu, Liu Rongke, Dai Bin, et al. Path splitting selecting strategy-aided successive cancellation list algorithm for polar codes[J]. IEEE Communications Letters, 2019, 23(3): 422-425.”.

[0043] Since the PS-SS-SCL (1) decoding method constructs a key set by selecting the first bit of all rate 1 nodes, and the PS-SS-SCL (2) decoding method constructs a key set by selecting the first and second bits of all rate 1 nodes, both methods only consider the reliability of the polarization channel and do not consider the error impact of the information bit with the lowest Hamming weight on the decoding. Therefore, the present invention comprehensively considers both and calculates the channel reliability according to the polarization weight method, and proposes a simplified SCL decoding method based on a key set with low complexity and low method loss.

[0044] In order to verify the superiority of the complexity of the flip set of the present invention over the key set in the literature [1], the number of bits that need to be copied, sorted and deleted during decoding is used as the complexity for analysis. The computational complexity of the traditional unsimplified SCL decoding method, the CS-SCL decoding method proposed in the present invention, and the PS-SS-SCL (1) decoding method and the PS-SS-SCL (2) decoding method proposed in the literature [1] are statistically analyzed when the code length is 1024 and 512, as shown in Table 1.

[0045] Table 1 Statistics of computational complexity of four methods

[0046]

[0047] As shown in Table 1, the computational complexity of the CS-SCL method proposed in the present invention is reduced by at least 70% when N=1024 and 512 compared to the traditional SCL decoding method. Compared with PS-SS-SCL (2), which has a smaller loss in error correction performance among the PS-SS-SCL decoding methods, the computational complexity of the CS-SCL decoding method proposed in the present invention is also reduced, by 6.1% and 6.2% when N=1024 and 512, respectively. Combining the computational complexity and error correction performance, the proposed method can effectively reduce the computational complexity of decoding with minimal loss in error correction performance. Furthermore, since the value of the variable a introduced in the proposed method can be flexibly selected, the computational complexity can be further reduced, but at the cost of a greater loss in error correction performance.

[0048] Figure 3 The following is a simulation result comparing the error correction performance of the four methods when N=1024 and a=20. Figure 4 The error correction performance comparison chart of the four methods when N = 512. Other simulation parameters are set the same, that is, the maximum number of decoding lists L = 8, the code rate R = 1 / 2, and the CRC generator polynomial g(x) = x 16 +x 12 +x 6 +x 5 +x+1, all methods use BPSK modulation, and the channel uses additive white Gaussian noise channel.

[0049] Depend on Figure 3 It can be seen that compared with the original SCL decoding method, the error correction performance loss of the method proposed in the present invention is the smallest. When the code length is 1024 and BLER=10 -5 When the PS-SS-SCL (1) decoding method has a performance loss of 0.12dB, the PS-SS-SCL (2) method has a performance loss of 0.07dB, and the CS-SCL decoding method proposed in the present invention has a loss of about 0.02dB, which is a 0.05dB gain compared to the PS-SS-SCL (2) method.

[0050] Depend on Figure 4 It can be seen that the error correction performance of the method proposed in the present invention is the least lost compared with the original SCL decoding method. When the code length is 512 and BLER=10 -5 When the error correction performance loss is large, the PS-SS-SCL (1) decoding method proposed in the literature [1] has a performance loss of 0.25dB, and the PS-SS-SCL (2) decoding method has a performance loss of 0.13dB. The CS-SCL method proposed in the present invention has almost no loss, and has a gain of 0.13dB compared with the PS-SS-SCL (2) decoding method.

Claims

1. A simplified SCL (Successive Cancellation List of Polar Codes Based on Critical Sets) decoding method for polar codes, characterized by: To address the high computational complexity of the Successive Cancellation List (SCL) decoder, a key set is constructed based on the channel characteristics of polar codes, taking into account the minimum Hamming Weight (MHW) of the information bits and channel reliability. Information bits within the key set are still decoded using SCL and path splitting, while information bits outside the key set are directly hard-determined without path splitting. This method specifically includes the following steps: Step 1: Select the polar code length N, the number of information bits m, and the number of cyclic redundancy check (CRC) bits r to be designed. For a given subchannel index i, its binary expansion is B = (b n-1 ,...,b1,b0), then the polarization weight (PW) corresponding to subchannel i is defined as formula (1): The polarization weight method is used to calculate the polarization weight value of each split channel. Among them, the PW value of 0 indicates that the channel transmits frozen bits, and the positive PW value indicates that the channel transmits non-frozen bits. The larger the PW value, the more reliable the channel. All split channels are sorted from high to low according to the channel reliability. The sorted split channel position index value sequence is obtained, and the first m+r split channels with the largest reliability are selected, that is, The split channels corresponding to the first m+r index values ​​are used as the non-frozen bit set A, and the remaining Nmr split channels are used as the frozen bit set A (usually set to 0). c ; Step 2: Sequence Perform CRC encoding, Add r bits of CRC check code at the end to check all the previous bits to get the sequence Step 3: Sequence Polar code encoding is performed, and the sequence As a non-frozen bit, it is input into the polar code encoder for polar code encoding to obtain the polar code encoded codeword Then Incoming channel for transmission; Step 4: Decompose the polar code into 6 sub-polar codes. The code length of the first and last sub-polar codes is N = 2. n-2 , corresponding to the smallest and largest parts of the bit index respectively, and the code length of the remaining four sub-polar codes is N = 2 n-3 , located between two longer sub-polar codes; The definitions of MHW set and sub-minimum HMW set are: Among them, the generator matrix G N The Hamming weight value of the i-th row in is the number of elements 1, d in formulas (2) and (3) m and d s denote the MHW and sub-MHW of the non-frozen bit set respectively; The index value of the MHW bit in each sub-polar code with formula (2) is included in the key set. If the number of bits with MHW in the sub-polar code is less than 1% (rounded off) of the number of elements in the non-frozen bit set, the index of the bit with the secondary MHW shown in formula (3) in the sub-polar code is also included in the key set. Step 5: Use the polarization weight method to calculate the polarization weight value of each channel, thereby sorting the channel reliability from small to large. Variable a is referenced to control the number of low-reliability channels. Channel indices with low polarization weight values ​​among a% of non-frozen bits are added to the key set. a can be flexibly selected based on the target block error rate. If the error correction performance requirement is high, then when the block error rate is almost unchanged (compared to the original SCL decoding method without path reduction), the channels with the minimum percentage of low PW values ​​are added to the key set. If the error correction performance requirement is low, then the channels with a% of low PW values ​​are added to the key set based on the target block error rate. Step 6: Decoding. The receiver first converts the received signal into a log-likelihood ratio (LLR) and then calculates the decision LLR for each bit. The information bits in the key set are still decoded using SCL, and path splitting is performed to retain both "0" and "1" results of the bit. The path metric (PM) value is updated according to the LLR according to formula (4). The larger the path metric value, the smaller the confidence of the corresponding decoding path. In practical applications, in order to facilitate hardware implementation, formula (5) can be used to simplify the expression: The information bits outside the key set are directly hard-determined, and the bit decision criterion is as follows: After decoding is completed, the path with the smallest PM is selected from the paths that pass the CRC check as the output result of the decoder.

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