Improved method for high-performance bp decoding of polar codes

Abstract

This invention relates to polar code technology in the field of channel coding, and discloses a high-performance BP decoding improvement method for polar codes. This method first initializes the decoding information; then, it uses a piecewise fitting function to update each node in the factor graph (…). i , j The left and right information of ) until the number of iterations. t The maximum number of iterations is equal to the maximum number of iterations. Finally, a hard decision is made using the log-likelihood ratio, and the decoding result is output. The error rate performance of this method is similar to that of the original BP decoding, and better than the minimum sum algorithm and the improved minimum sum algorithm; however, the decoding complexity is less than that of the original BP decoding method.

Description

Technical Field

[0001] This invention relates to polar code technology in the field of channel coding, and particularly to a high-performance BP decoding improvement method for polar codes. Background Technology

[0002] The core purpose of communication is to effectively and reliably transmit information generated by the information source to the information destination. However, information is inevitably subject to various noise interferences during transmission. Channel coding technology introduces check symbols into the original information to detect and correct transmission errors, becoming one of the core means to improve communication reliability.

[0003] The polar codes proposed by Arıkan in 2008 are not only the first channel coding method that has been rigorously proven in theory to meet the Shannon capacity limit, but also have outstanding advantages such as clear structure, low complexity of encoding and decoding algorithms, and no error layer. Since its proposal, it has quickly become the core and hot topic of research in the field of channel coding, and has been successfully applied to 5G enhanced mobile broadband (eMBB) communication scenarios as a channel coding scheme for control information transmission.

[0004] In practical applications of polar codes, the performance of the decoding algorithm directly determines the final communication effect of the polar code. Different decoding algorithms exhibit differences in complexity, decoding delay, and error rate performance. The complexity of the Successive Cancellation (SC) decoding algorithm is... However, the SC decoding algorithm and its improvements are essentially serial, resulting in long decoding delays and hindering high throughput. Let n be the code length of the polar code, and n be a positive integer. Belief propagation (BP) decoding, another important method for polar code decoding, effectively reduces decoding latency due to its inherent parallel computing architecture. Furthermore, it exhibits good error handling performance through iterative message updates. However, the original BP decoding algorithm requires multiple iterations and employs complex nonlinear functions to calculate the iterative information for each node, resulting in a complexity of O(n^2). , where T is the number of iterations.

[0005] Therefore, without sacrificing performance, it is urgent to reduce the complexity of the original BP decoding algorithm and make it easier to implement in hardware. The main approach currently adopted is to simplify the complex nonlinear function that calculates the iterative information to reduce the complexity of the original BP decoding, such as the Min-Sum (MS) algorithm and the Improved-MS algorithm. However, these algorithms sacrifice some error rate performance while reducing complexity.

[0006] The MS algorithm simplifies the complex iterative information calculation formula into a comparison operation, greatly reducing complexity, but causing a loss in error rate performance. The Improve-MS algorithm performs piecewise fitting on the complex iterative information calculation formula, specifically by zeroing or offset compensation of the MS operation to reduce fitting error, thereby minimizing the impact on error rate performance while reducing computational complexity. However, the iterative information update formulas used by these methods all have certain fitting errors compared to the iterative information update formula of the original BP decoding algorithm, resulting in a deterioration in error rate performance. Summary of the Invention

[0007] This invention addresses the shortcomings of existing primitive BP decoding methods for polar codes by providing a high-performance improved BP decoding method for polar codes. This method improves the BP decoding method by analyzing the update formula of iterative information. Properties of the function, where x and y are real numbers, for the function Piecewise fitting was performed, resulting in a small fitting error and simple calculation of the fitting function. Therefore, this method has similar error performance to the original BP decoding, but with lower complexity, especially in the medium to high signal-to-noise ratio region.

[0008] This invention provides an improved high-performance BP decoding method for polar codes, comprising: Step 1. Decoding information initialization: Step 1-1. The sending end constructs a code length of N, an information bit count of K, and an information set of... Frozen set The polar code, in which, , Code length n is a positive integer; Step 1-2. Generate message sequence The index belongs to The location transmits K information bits, and the index belongs to The location is transmitted with NK frozen bits. The value of the frozen bits is known to the receiver and is 0 by default. Steps 1-3. For Polar code encoding is performed to obtain the codeword sequence. ,in , , This is a bit-flipping matrix. express The nth Kronecker product; Steps 1-4. The receiving end receives the sequence after transmission through the channel and calculates each coded bit. The corresponding log-likelihood ratio (LLR) value of the channel information Let the decoding factor graph be And set the maximum number of iterations for the decoder to be The current iteration number t=1, where ; Steps 1-5. Initialize the left information of each node (i,j) in the decoding factor graph. And right information , , , where i is the index of the stage in the polar code factor graph. , where j is the index of the row in the polar code factor graph. ; Step 2. Iteratively update the left and right information of each node (i,j): Step 2-1. Update the left information of each node from right to left on the factor graph. ; Step 2-2. Update the right information of each node from left to right on the factor graph. ; One iteration of BP decoding involves: information first being passed from the rightmost node to the leftmost node, and then from the leftmost node to the rightmost node. The specific expression is as follows: When x and y satisfy the condition hour, ,in, , For function The 11-segment fitting function, The specific expression is: , Where e is the natural constant; When x and y satisfy the condition , ,in, ; Step 3. If the current iteration number t satisfies If so, return to step 2, continue to the next iteration, and let If satisfied Then proceed to step 4; Step 4. Output the decoding result , where each bit The hard verdict was , .

[0009] Compared with the prior art, the advantages of the present invention are as follows: 1. The high-performance BP decoding improvement method for polar codes provided by this invention performs piecewise fitting of the original iterative information update formula, wherein the computational complexity of the fitting function used in each segment is much lower than that of the original iterative information update formula, and the fitting error is smaller compared with the MS algorithm and Improve-MS algorithm; 2. The high-performance BP decoding improvement method for polar codes provided by this invention has a decoding complexity much lower than the original BP decoding method, especially in the medium-to-high signal-to-noise ratio region, and has similar error performance as the original BP decoding. 3. The high-performance BP decoding improvement method for polar codes provided by this invention has better error performance than the MS algorithm and the Improve-MS algorithm. Attached Figure Description

[0010] Figure 1 The flowchart illustrates an improved high-performance BP decoding method for polar codes provided by this invention.

[0011] Figure 2 The graph shows the BER performance comparison of the high-performance BP decoding improvement method for polar codes provided by this invention with the original BP decoding algorithm, MS algorithm, and Improve-MS algorithm at different iteration numbers, with a code length N=256 and a code rate of 0.5.

[0012] Figure 3 The graph shows the BLER performance comparison of the high-performance BP decoding improvement method for polar codes provided by this invention with the original BP decoding algorithm, MS algorithm, and Improve-MS algorithm at different iteration numbers, with a code length N=256 and a code rate of 0.5.

[0013] Figure 4 The graph shows the BER performance comparison of the high-performance BP decoding improvement method for polar codes provided by this invention with the original BP decoding algorithm, MS algorithm, and Improve-MS algorithm at different iteration numbers, with a code length N=512 and a code rate of 0.5.

[0014] Figure 5 The graph shows the BLER performance comparison of the high-performance BP decoding improvement method for polar codes provided by this invention with the original BP decoding algorithm, MS algorithm, and Improve-MS algorithm at different iteration numbers, with a code length N=512 and a code rate of 0.5.

[0015] Figure 6 The graph shows the BER performance comparison of the high-performance BP decoding improvement method for polar codes provided by this invention with the original BP decoding algorithm, MS algorithm, and Improve-MS algorithm at different iteration numbers, with a code length N=1024 and a code rate of 0.5.

[0016] Figure 7The graph shows the BLER performance comparison of the high-performance BP decoding improvement method for polar codes provided by this invention with the original BP decoding algorithm, MS algorithm, and Improve-MS algorithm at different iteration numbers, with a code length N=1024 and a code rate of 0.5. Detailed Implementation

[0017] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples; the following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0018] Example 1: To reduce the complexity of iterative information updates in the original BP decoding, this example provides a function. Piecewise fitting function: (1) When , , For function The 11-segment fitting function, ,when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, where e is the natural constant; (2) When , .

[0019] Example 2: Based on the piecewise fitting function of the iterative information update formula obtained in Example 1, this invention provides a high-performance BP decoding improvement method for polar codes. The specific steps are as follows: Step 1. Decoding information initialization: Step 1-1. The sending end constructs a code length of N, an information bit count of K, and an information set of... Frozen set The polar code, in which, , Code length n is a positive integer; Step 1-2. Generate message sequence The index belongs to The location transmits K information bits, and the index belongs to The location is transmitted with NK frozen bits. The value of the frozen bits is known to the receiver and is 0 by default. Steps 1-3. For Polar code encoding is performed to obtain the codeword sequence. ,in , , This is a bit-flipping matrix. express The nth Kronecker product; Steps 1-4. The receiving end receives the sequence after transmission through the channel and calculates each coded bit. The corresponding log-likelihood ratio (LLR) value of the channel information Let the decoding factor graph be And set the maximum number of iterations for the decoder to be The current iteration number t=1, where ; Steps 1-5. Initialize the left information of each node (i,j) in the decoding factor graph. And right information , , , where i is the index of the stage in the polar code factor graph. , where j is the index of the row in the polar code factor graph. ; Step 2. Using the method described in Example 1 In the decoding factor graph, the piecewise fitting function first updates the left information of each node (i,j) from right to left. Then, update the right information of each node (i,j) from left to right. Where t is the current iteration number; Step 3. If the current iteration number t satisfies If so, return to step 2, continue to the next iteration, and let If satisfied Then proceed to step 4; Step 4. Output the decoding result , where each bit The hard verdict was , .

[0020] Because the iterative information update formula of the original BP decoding is piecewise fitted, the computational complexity of the high-performance BP decoding improvement method for polar codes provided by this invention is much smaller than that of the original BP decoding. Table 1 shows the running time of different decoding algorithms on a computer (16G memory, i7-11700F CPU, 2.5GHz CPU frequency, and 4.9GHz maximum turbo frequency) under different signal-to-noise ratios with a code length of 1024. The time is the average computation time per frame obtained by the algorithm in 5000 frame decoding simulations under the signal-to-noise ratio. Each frame in the simulation is executed 50 times.

[0021] Table 1 shows the running time of different decoding algorithms when the code length is 1024. .

[0022] In the second embodiment of the present invention, a specific example of a high-performance BP decoding improvement method using a polar code is as follows: Step 1. Decoding information initialization: The transmitting end uses the Gaussian approximation algorithm to construct a code length of N=8, an information bit count of K=4, and an information set of... Frozen set The polar code, which carries a sequence of messages. After polar code encoding, the codeword sequence is obtained. ,in , , This is a bit-flipping matrix. express The signal-to-noise ratio of the Gaussian approximation algorithm for the cubic Kronecker product is -0.5dB. Gaussian approximation algorithm: Under SC decoding conditions, calculate each polarization channel mean LLR , The larger the polarization channel The more reliable; The recursive calculation formula is as follows: , in, , , The approximation is ; Based on the reliability of each polarization channel, K of the most reliable polarization channels are selected from the N polarization channels for transmitting information bits, and their indices constitute the information set. The remaining NK polarization channels transmit known fixed bits at the receiver, and their indices form a frozen set. ; After BPSK modulation ( After transmission through the AWGN channel, the sequence received by the receiver is: Calculate each coded bit Corresponding channel information ,make And set the maximum number of iterations for the decoder to be The current iteration number t=1, where , The noise variance of the AWGN channel; Initialize the left information of each node (i,j) in the decoding factor graph. And right information , , ,in This is the index of the stage in the polar code factor graph. , where j is the index of the row in the polar code factor graph. ; Step 2. Using the method described in Example 1 In the decoding factor graph, the piecewise fitting function first updates the left information of each node (i,j) from right to left. Then, update the right information of each node (i,j) from left to right. Where t is the current iteration number; Step 3. If the current iteration number t satisfies If so, return to step 2, continue to the next iteration, and let If satisfied Then proceed to step 4; Step 4. Output the decoding result , where each bit The hard verdict was , .

[0023] In summary, the first embodiment of this invention performs piecewise fitting on the iterative information update formula in the original BP decoding, using a function with low computational complexity to reduce decoding complexity and achieve a small fitting error. Then, the second embodiment of this invention, based on the first embodiment, provides an improved high-performance BP decoding method for polar codes. Numerical results show that the error rate performance of the improved high-performance BP decoding method for polar codes provided by this invention is similar to that of the original BP decoding, and superior to the MS algorithm and the Improved-MS algorithm, but with lower decoding complexity than the original BP decoding method.

[0024] The entire process of the high-performance BP decoding improvement method for polar codes provided by this invention is as follows: Figure 1As shown, first initialize the decoding information; then utilize... The piecewise fitting function updates the left and right information of each node (i,j) until the number of iterations equals the maximum number of iterations. , , Finally, hard decision is made using the log-likelihood ratio, and the decoding result is output.

[0025] To verify the effectiveness of the present invention, numerical simulation experiments were conducted, and the error rate performance was compared with that of the MS algorithm, the Improved-MS algorithm, and the original BP decoding algorithm under the same conditions.

[0026] In the numerical simulation, the channel is an AWGN channel with BPSK modulation ( The encoding settings remain the same throughout; in all simulation diagrams, the signal-to-noise ratio of the AWGN channel is utilized. The error performance is represented using the bit error rate (BER) and the block error rate (BLER). The proposed high-performance BP decoding improvement method, MS algorithm, Improved-MS algorithm, and original BP decoding method provided in this invention are simplified as Proposed decoding, MS, Improved-MS, and BP, respectively. To ensure the accuracy of the simulation results, each... The BER and BLER calculations under these conditions included at least 200 error frames.

[0027] Figure 2 and Figure 3 The BER and BLER performance of all decoding methods at different iteration numbers are represented under the conditions of code length N=256 and code rate R=0.5, respectively. Figure 4 and Figure 5 The BER and BLER performance of all decoding methods at different iteration numbers are represented under the conditions of code length N=512 and code rate R=0.5, respectively. Figure 6 and Figure 7 The figures represent the BER and BLER performance of all decoding methods at different iteration numbers under the conditions of code length N=1024 and code rate R=0.5, respectively. Under different code lengths and different iteration numbers, the error rate performance of the high-performance BP decoding improvement method for polar codes provided by this invention is similar to that of the original BP decoding, and far superior to the MS algorithm and the Improved-MS algorithm.

[0028] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A high-performance BP decoding improvement method for polar codes, characterized in that, Includes the following steps: Step 1. Decoding information initialization: Step 1-1. The sending end constructs a code length of N, an information bit count of K, and an information set of... , frozen collection The polar code, in which, , Code length n is a positive integer; Step 1-2. Generate message sequence The index belongs to The location transmits K information bits, and the index belongs to The location is transmitted with NK frozen bits. The value of the frozen bits is known to the receiver and is 0 by default. Steps 1-3. For Polar code encoding is performed to obtain the codeword sequence. ,in , , This is a bit-flipping matrix. express The nth Kronecker product; Steps 1-4. The receiving end receives the sequence after transmission through the channel and calculates each coded bit. Corresponding channel information Let the decoding factor graph be And set the maximum number of iterations for the decoder to be The current iteration number t=1, where ; Steps 1-5. Initialize the left information of each node (i,j) in the decoding factor graph. And right information , , , where i is the index of the stage in the polar code factor graph. , where j is the index of the row in the polar code factor graph. ; Step 2. Iteratively update the left and right information of each node (i,j): Step 2-1. Update the left information of each node from right to left on the factor graph. ； Step 2-2. Update the right information of each node from left to right on the factor graph. ； One iteration of BP decoding includes: first, updating all left information from right to left, and then updating all right information from left to right; Iterative information update formula The specific expression depends on the magnitudes of the input variables x and y: when and When the value of is simultaneously less than the decoding threshold, ,in Is and When the value of is simultaneously less than the decoding threshold, the update formula for the original BP decoding iteration information is... The fitting approximation; when or When the value is greater than or equal to the decoding threshold, ,in Is or When the value of is greater than or equal to the decoding threshold, the update formula for the original BP decoding iteration information is as follows: The fitting approximation; Step 3. If the current iteration number t satisfies If so, return to step 2, continue to the next iteration, and let If satisfied Then proceed to step 4; Step 4. Output the decoding result. , where each bit The hard verdict was , .

2. The improved high-performance BP decoding method for polar codes according to claim 1, characterized in that, Channel information calculated in step 1 The left information of each node (i,j) updated in step 2. And right information Both are values ​​in log-likelihood ratio form, where, , t is the current iteration number.

3. The improved high-performance BP decoding method for polar codes according to claim 1, characterized in that, In step 2, when updating the left and right information of each node (i,j), where, , The decoding threshold is set to 36, and the iterative information update formula is... The relationship between the values ​​of input variables x and y is as follows: If the values ​​of input variables x and y satisfy the condition ,but ; If the values ​​of input variables x and y satisfy the condition ,but .

4. The improved high-performance BP decoding method for polar codes according to claim 1, characterized in that, In step 2, when updating the left and right information of each node (i,j), where, , , and The specific expression is: ,in For function The 11-segment fitting function, The specific fitting function used is: in the interval and Inside, Using a constant a; in the interval Inside, Using logarithmic functions ; in the interval Inside, Using the reciprocal function ; in the interval Inside, Using exponential function form , where e is the natural constant, and a, b, and c are the fitting parameters; 。 5. The method according to claim 4, characterized in that, functions in The specific expression is: 。

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