An improved polar code EPC-MS-SCL decoding method

Abstract

The present invention specifically relates to an improved polar code EPC‑MS‑SCL decoding method based on an enhanced parity check code. The present invention belongs to the technical field of channel coding. The method performs segmentation processing on the information sequence in the polar code encoding stage, adds an enhanced parity check code at the end of each segment, and the decoder only performs path splitting when decoding elements in the search set (SS). The remaining elements directly perform hard decision decoding, and immediately verify the segment after decoding a sequence. Only the path that passes the verification is retained, which reduces the competition of the wrong path for the correct path, increases the probability that the correct path is retained until the end of decoding, and reduces the number of decoding lists, so that the decoding complexity is lower. Simulation results show that the improved polar code EPC‑MS‑SCL decoding method proposed in the present invention has obvious decoding performance improvement and reduced decoding complexity compared with the decoding method based on the path splitting strategy assisted polar code serial cancellation list (PSS‑SS‑SCL).

Description

Technical Field

[0001] The present invention belongs to the technical field of channel coding, and relates to an improvement of a polar code decoding method based on a path splitting strategy auxiliary serial cancellation list (Path Splitting Selecting Strategy based on Search Set under the Successive Cancellation List, PSS-SS-SCL) in channel coding. The method is mainly based on the principle of an enhanced parity check code and a polar code serial cancellation list (Successive Cancellation list, SCL) decoding method to improve the PSS-SS-SCL decoding method. Background Art

[0002] Polar codes were proposed by Arikan. They are the first type of codewords that can be proven to reach the channel capacity of binary input memoryless symmetric channels and are an important technology for the next generation of mobile communication systems. Polar codes have been successfully selected into the 5G standard and have become the coding scheme for control channels in 5G enhanced mobile broadband scenarios. They are a research hotspot in the current field of channel coding. In addition to the channel capacity achievable characteristics, the outstanding advantage of polar codes is that there is no error floor under the serial cancellation decoding algorithm. However, in the case of limited code length, due to incomplete channel polarization, the actual SC decoding algorithm's block error rate (BLER) performance is much worse than that of Turbo codes and LDPC codes.

[0003] Therefore, some researchers proposed a serial cancellation list (SCL) decoding algorithm that can retain multiple decoding paths, and a CA-SCL (CRC Aid SCL) decoding algorithm that uses a CRC-Polar code cascaded with a cyclic redundancy check (CRC) code. The CA-SCL decoding algorithm selects the codeword that passes the CRC check and has the optimal path metric as the decoding output at the end of decoding, which improves the decoding performance of SCL. It is also the current mainstream polar code decoding scheme. Under the CA-SCL decoder, compared with the LDPC code of the same code length and code rate, the BLER performance of the polar code can exceed the existing LDPC code. Although CA-SCL has good decoding performance, the algorithm has a high decoding complexity of O(LNlogN), where L is the size of the decoder list and N is the length of the polar code codeword. In order to reduce the decoding complexity of CA-SCL, researchers have proposed corresponding improvement schemes. Since there are significant differences in the reliability of different bits of polar codes, it is not necessary to split all information bits. Based on this, some scholars have proposed a PSS-SS-SCL decoding method based on a path splitting strategy. This method only performs path splitting when decoding elements in the search set (SS). With almost the same performance as CA-SCL, a lower decoding complexity is obtained. However, the PSS-SS-SCL decoding method based on the path splitting strategy does not consider how to improve the decoding success rate at the split bit position, so compared with CA-SCL, no improvement in decoding performance is achieved. In response to this problem, the present invention improves the decoding success rate of the position by adding an enhanced parity check code before the error-prone position and performing check pruning immediately after decoding a section, thereby proposing an EPC-MS-SCL (Enhanced Parity Check and Monte Carlo Segement aided Successive Cancellation List) decoding algorithm that not only retains the low splitting number characteristics of the PSS-SS-SCL decoding method but also achieves better decoding performance. Summary of the invention

[0004] In view of this, the object of the present invention is to provide an improved polar code EPC-MS-SCL decoding method. By segmenting the information sequence in the polar code encoding stage, an enhanced parity check code is added at the end of each segment. The decoder only performs path splitting when decoding elements in the search set, and directly performs hard decision decoding on the remaining elements. After decoding a segment of the sequence, the segment is checked and the paths that fail the check are cut off, thereby reducing the competition of the wrong path for the correct path and increasing the probability that the correct path is retained until the end of decoding, thereby improving the decoding performance and reducing the number of decoding lists, making the decoding complexity lower.

[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 k, the number of bits of the enhanced parity check code m, and the number of bits of the CRC code w to be designed are selected. The reliability metric value of each channel is calculated using the Gaussian approximation method and sorted from high to low to obtain the split channel position index value sequence And determine the frozen bit set A c and the non-frozen bit set A and the search set SS.

[0007] Then, Monte Carlo simulation experiments are used to count the error rates of the SS set elements, and the first m elements with the highest error rates are selected and the enhanced check codes are placed in sequence to complete the information sequence. The segmented processing obtains the sequence will sequence Perform CRC encoding to obtain the sequence Then the sequence As a non-frozen bit set, it is input into the polar code encoder to obtain the polar code codeword And put the codeword into the channel for transmission.

[0008] Then, the corresponding decoding method is adopted at the receiving end, that is, the decoder only performs path splitting when decoding SS set elements, and immediately verifies all current paths after decoding a sequence, and cuts off the paths that fail the verification.

[0009] Finally, in the same simulation environment, a simulation comparison and analysis is performed between an improved polar code EPC-MS-SCL decoding method proposed in this patent and other similar decoding methods.

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

[0011] An improved polar code EPC-MS-SCL decoding method is proposed. In this method, the information sequence is first segmented in the polar code encoding stage, and then an enhanced parity check code is added at the end of each segment. The decoder only performs path splitting when decoding elements in the search set, and directly performs hard decision decoding on the remaining elements. After decoding a segment of the sequence, the segment is immediately checked, and only the path that passes the check is retained. This method has the following advantages: 1. It reduces the competition of the wrong path for the correct path, increases the probability that the correct path is retained until the end of decoding, and improves the decoding performance; 2. It reduces the number of decoding lists, making the decoding complexity lower; 3. Verification can be performed during the decoding process, and when no path passes the check, the decoder can stop the subsequent unnecessary decoding operations. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0014] Figure 2 Schematic diagram of a binary tree with a polar code length of 16;

[0015] Figure 3 Schematic diagram of an enhanced parity check code with a check sequence length of 8 and a check code length of 2;

[0016] Figure 4 The polar code length is 256, the information sequence length is 128, an 8-bit enhanced parity check code and a segmented schematic diagram of an 8-bit CRC check code are used;

[0017] Figure 5 The bit error rate performance comparison chart of four polar code decoding methods;

[0018] Figure 6 is the average total number of decoding lists for different decoding methods;

[0019] Figure 7 is the average number of decoding splits for different decoding methods;

[0020] Figure 8 is the average number of decoding rankings for different decoding methods. DETAILED DESCRIPTION

[0021] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0022] 1) Combined with Figure 1 It is explained that the specific implementation method of an improved polar code EPC-MS-SCL decoding method is as follows:

[0023] In the polar code encoding stage, the code length N of the polar code to be designed is first determined, and the reliability measurement parameter of each split channel is calculated using the Gaussian approximation method. All split channels are sorted from high to low according to the channel reliability to obtain the sorted split channel position index value sequence. Select the first k+m+w split channels with the greatest reliability, that is, The split channels corresponding to the first k+m+w index values ​​are used as the non-frozen bit set A, and the remaining Nkmw split channels are used as the frozen bit set A. c , where k is the number of information bits contained in a codeword, m is the number of bits of the selected enhanced parity check code, and w is the number of bits of the added CRC. cThus, the R1 node distribution is obtained, and the first element of each R1 node is selected to obtain the SS set.

[0024] At the receiving end, the value of the received signal is first converted into a log-likelihood ratio (LLR), as shown in equation (4).

[0025]

[0026] In formula (4), y i represents the received signal value of each bit, σ 2 represents the variance of the channel noise.

[0027] Each path then obtains the decision LLR for each bit by performing the corresponding f and g operations.

[0028] L≈sign(L1)sign(L2)min{|L1||L2|}(5)

[0029] L=(1-2U1)L1+L2 (6)

[0030] 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 of the operation output; L1, L2 represent the LLR of the input operation, and U1 represents the decoded estimated value of the previous bit of the input operation.

[0031] If the current bit belongs to A c , then each path directly translates the bit value to 0; if the current bit belongs to the SS set, each path directly performs hard decision decoding; in other cases, ordinary SCL decoding is performed. After decoding a sequence, the information sequence of the segment is immediately checked through the enhanced parity check code of the segment, and only the paths that pass the check are retained. If no path passes the check, the decoding is declared a failure. Finally, after the decoding is completed, the path that passes the CRC check and has the optimal path metric value is selected as the decoding output result.

[0032] 2) Combine with attachment Figure 2 Explain the selection of search set:

[0033] The polar code can be regarded as consisting of multiple sub-polar code blocks, in which the sub-block containing only information bits is called R1 node. In the figure, the white nodes are frozen bit nodes, the gray nodes are mixed nodes, and the black nodes are information bit nodes. The R1 nodes are {A, B, C, D, E}, and the first element is taken to form the SS set {u1, u2, u3, u5, u6}.

[0034] 3) Combine with attachment Figure 3 Explain the construction of enhanced parity check code:

[0035] The enhanced parity check code uses multiple check bits, where each check bit is the parity check of some bits in the information sequence. The value of the first check bit is determined by the sequence. All elements are encoded by traditional parity check. The value of the second check bit is obtained by parity check encoding of the odd bits in the sequence checked by the first check code; the value of the nth check bit is obtained by parity check encoding of the odd bits in the n-1th check sequence; the error detection capability of the enhanced parity check code is analyzed by taking the two-bit check code as an example: when the sequence An odd number of errors can be detected by the first check bit; when the sequence There are an even number of errors in the sequence There are two situations: odd number of errors in the odd bits and even number of errors in the even bits. The former situation can be detected by the second check bit.

[0036] Therefore, the two-bit enhanced parity check code can detect all odd errors and half of the even errors, and the error detection capability is: 3 / 4. For the n-bit enhanced parity check code, its error detection capability is derived as: (n is the number of bits of the check code).

[0037] 4) Combine with attachment Figure 4 Description: Segment the information sequence and add a checksum:

[0038] The elements in the SS set are used to estimate the error rate through Monte Carlo simulation experiments: i When there is a correct path before decoding and decoding S i There is also a correct path after that, then the decoding is recorded in S i If the decoding S i If there is no correct path after that, then the decoding is recorded in S i Failure occurs at the first position, and finally the probability of decoding failure of each element is obtained by statistics. Then select the first m bits with higher error rates, and then arrange the m bits in ascending order according to the channel position. The first element is judged by the number of information bits before the position. If there is no information bit before, skip the element; if the number of information bits is less than 5, place 1 check bit in the first segment; otherwise, place 2 check bits. The remaining elements are compared with the difference with the previous element. If it is equal to 1, skip the current element; if it is less than 5, place 1 check bit at the end of the information sequence; otherwise, place 2 check bits at the end of the information sequence, until m check bits are placed, then the information sequence is completed. Add enhanced parity check code segment by segment and get sequence Then the sequence Send to CRC encoder to get the added sequence Will As a non-frozen bit sequence, it is input into the polar code encoder to obtain the polar code codeword P1 N , and input the codeword into the channel for transmission.

[0039] 5) Combine with attachment Figure 5 , 6, 7, 8 demonstrate the superiority of the proposed decoding method, as follows:

[0040] The CA-SCL decoding method is a scheme proposed in the literature [1] "NIU K, CHEN K. CRC-Aided Decoding of Polar Codes [J]. IEEE Communications Letters, 2012, 16 (10): 1668-1671."

[0041] The PSS-SS-SCL decoding method is a scheme proposed in the literature [2] "GAO C, LIU R, DAI B, HAN X. Path Splitting Selecting Strategy-Aided Successive Cancellation List Algorithm for Polar Codes [J]. IEEE Communications Letters, 2019, 23 (3): 422-425."

[0042] The Segment-CRC decoding method is the solution proposed in the literature [3] "ZHOU H, ZHANG C, SONG W, Xu S, YOU X, Segmented CRC-Aided SC List Polar Decoding[C] / / 2016 83rd Vehicular Technology Conference (VTC Spring). Nanjing: IEEE, 2016: 1-5."

[0043] The initial conditions of the simulation are set to polar code length N = 256, K = 128, and code rate The number of decoding lists L is 8, and the CA-SCL and PSS-SS-SCL decoding methods use a 16-bit CRC check code g 16 (x) = x 16 +x 15 +x 2 +1; Segement-CRC decoding method divides the information sequence into 4 segments evenly, and each segment uses a 4-bit CRC check code g4(x)=x 4+x+1; EPC-MS-SCL decoding method uses 8-bit PC and 8-bit CRC check code g8(x)=x 8 +x 5 +x 4 +1, the channel uses the additive white Gaussian noise channel (AWGN). Figure 5 It can be seen that the EPC-MS-SCL decoding method proposed in the present invention has improved performance compared with the other three decoding methods, among which the EPC-MS-SCL decoding method has a better performance when BLER=10 -3 Compared with CA-SCL and PSS-SS-SCL decoding methods, the gain is improved by about 0.12dB and 0.2dB respectively; at BLER=10 -4 Compared with CA-SCL and PSS-SS-SCL decoding methods, the gain is increased by about 0.1dB and 0.22dB respectively. Figure 6 It can be seen that the EPC-MS-SCL decoding method proposed in this paper has a lower average number of decoding lists than the traditional CA-SCL and PSS-SS-SCL decoding methods, and is only slightly higher than the Segment-CRC decoding method. When L=32, the EPC-MS-SCL decoding method reduces the number of decoding lists by about 5% compared with the traditional CA-SCL and PSS-SS-SCL decoding methods. Figure 7 It can be seen that the number of splits of EPC-MS-SCL and PSS-SS-SCL is almost the same, and compared with CA-SCL, the Segment-CRC decoding method reduces the number of splits by about 70%. The reason why the number of splits is slightly lower than that of PSS-SS-SCL when L is 2 is that the segment check has an early termination function. After a certain segment is decoded, if no path passes the check, the subsequent decoding steps will be stopped. Figure 8 It can be seen that the average sorting times of the EPC-MS-SCL decoding method is reduced by about 79% compared with the traditional CA-SCL decoding method, and is lower than the Segment-CRC and PSS-SS-SCL decoding methods, with the least sorting times. In summary, the EPC-MS-SCL decoding method proposed in this paper not only retains the advantages of low splitting times and low sorting times compared with the PSS-SS-SCL decoding method, but also significantly improves the decoding performance of the PSS-SS-SCL decoding method.

Claims

1. An improved polar code EPC-MS-SCL (Enhanced Parity Check and Monte Carlo Segement aided Successive Cancellation List) decoding method, characterized by: Aiming at the problem of insufficient performance of the decoding method based on path splitting selecting strategy based on search set under the successive cancellation list (PSS-SS-SCL) in polar code, the information sequence is segmented in the polar code encoding stage, and an enhanced parity check code (EPC) is added at the end of each segment. The decoder only performs path splitting when decoding elements in the search set (SS), and directly performs hard decision decoding on the remaining elements. After decoding a segment of the sequence, the segment is checked immediately, and only the path that passes the check is retained, thereby reducing the competition of the wrong path for the correct path, increasing the probability that the correct path is retained until the end of decoding, improving the decoding performance, and reducing the number of decoding lists at the same time, making the decoding complexity lower. An improved polar code EPC-MS-SCL decoding method specifically includes the following steps: Step 1: Channel reliability estimation. Select the polar code length N to be designed, use the Gaussian approximation method to calculate the reliability measurement parameter of each split channel, sort all split channels from high to low according to the channel reliability, and obtain the sorted split channel position index value sequence. Step 2: Determine the non-frozen bit set A and the frozen bit set A c And the search set (SS), select the first k+m+w split channels with the largest reliability, that is, The split channels corresponding to the first k+m+w index values ​​are used as the non-frozen bit set A, and the remaining Nkmw split channels are used as the frozen bit set A. c , where k is the number of information bits contained in a codeword, m represents the number of bits of the selected enhanced parity check code, and w represents the number of bits of the added cyclic redundancy check code (CRC). c Then determine the search set SS; Step 3: Count the error rates of the elements in the SS set and use Monte Carlo simulation to estimate the error rates of the elements in the SS set: i When there is a correct path before decoding and decoding S i There is also a correct path after that, then the decoding is recorded in S i If the decoding S i If there is no correct path after that, then the decoding is recorded in S i The decoding failure probability of each element is finally obtained by statistics; Step 4: Information Sequence Segment and add m bits of enhanced parity check code to get the segmented sequence Step 5: Sequence Perform CRC encoding. Add w bits of CRC check code at the end to check all the previous bits to get the sequence Step 6: 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 code word P1 N , and then P1 N Incoming channel for transmission; Step 7: Decoding: At the receiving end, the corresponding EPC-MS-SCL decoder is used to decode the received signal; The specific description of the segmentation of the information sequence and the addition of the EPC code in step 4 and the corresponding EPC-MS-SCL decoder in step 7 is as follows: 1) Enhanced parity check code, which uses multiple check bits, where a certain check bit is the parity check of certain bits in the information sequence; the value of the first check bit of the enhanced parity check code is obtained by performing traditional parity check coding on all elements of the sequence to be checked, the value of the second check bit is obtained by performing parity check coding on the odd bits in the sequence checked by the first check code, and the value of the nth check bit is obtained by performing parity check coding on the odd bits in the sequence checked by the n-1th check code; suppose the sequence to be checked is At this time, the i-th check bit m i The value of is obtained by equation (1), equation (2) and equation (3), where [] represents the floor rounding function; The error detection capability of the enhanced parity check code is analyzed, taking the two-bit check code as an example: when the sequence An odd number of errors can be detected by m1; when the sequence There are even number of errors in the sequence There are two situations: odd number of errors and even number of errors in the odd and even bits respectively. The former situation can be detected by m2. Therefore, the two-bit enhanced parity check code can detect all odd errors and half of the even errors. The error detection capability is: For an n-bit enhanced parity check code, its error detection capability is derived as: n is the number of bits of the check code; 2) For the segmentation of the information sequence, select the first m bits with higher error rates in the SS set, and then arrange the m bits in ascending order according to the channel position. The first element is judged by the number of information bits before the position. If there is no information bit before, skip the element; if the number of information bits is less than 5, place 1 check bit in the first segment; otherwise, place 2 check bits, and compare the difference between the remaining elements and the previous element. If it is equal to 1, skip the current element; if it is less than 5, place 1 check bit in the information sequence; otherwise, place 2 check bits in the information sequence until m check bits are placed. At this time, the segmented sequence is obtained. 3) The corresponding EPC-SS-SCL decoder, which first converts the received signal into a logarithm likelihood ratio (LLR) at the receiving end, and then calculates the decision LLR for each bit. If the current bit belongs to A c , each path directly translates the bit value to 0; if the current bit belongs to the SS set, each path directly performs hard decision decoding; in other cases, ordinary SCL decoding is performed, and the EPC-SS-SCL decoder will immediately verify the current sequence after decoding a sequence, and only retain the paths that pass the verification. If no path passes the verification, the decoding is declared a failure. If there are still decoding paths after all bits are decoded, the decoder will select the decoding path that passes the CRC check and has the largest path metric (PM) as the decoder's decoding output result.

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