Polarization code high-performance BP decoding improvement method

Abstract

The invention relates to a polarization code technology in the field of channel coding, and discloses a high-performance BP decoding improvement method of a polarization code. The method comprises the following steps: initializing decoding information; the left information and the right information of each node (i, j) in the factor graph are updated by using a piecewise fitting function until the number of iterations t is equal to the maximum number of iterations; and finally, performing hard decision by using a log-likelihood ratio, and outputting a decoding result. The error code performance of the method is close to that of original BP decoding and is superior to that of a minimum sum algorithm and an improved minimum sum algorithm; and the decoding complexity is smaller than that of the original BP decoding method.

Description

TECHNICAL FIELD

[0002] The present application relates to the field of polar code technology, in particular to an improved method for high-performance BP decoding of polar codes. BACKGROUND

[0003] The core purpose of communication is to effectively and reliably deliver the information generated by the source to the sink, but the information will inevitably be disturbed by various noises in the transmission process; channel coding technology introduces check symbols in the original information to realize the detection and correction of transmission errors, and becomes one of the core means to improve communication reliability.

[0004] Polar code proposed by Arikan in 2008 is not only the first type of channel coding method that is strictly proved to achieve the Shannon capacity limit in theory, but also has outstanding advantages such as clear structure, low complexity of encoding and decoding algorithm, and no error flat layer; since its proposal, it has rapidly become the research core and hotspot 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.

[0005] In the practical application of polar codes, the performance of the decoding algorithm directly determines the final communication effect of the polar codes, and different decoding algorithms show different characteristics in complexity, decoding delay, and error performance; the complexity of the Successive cancellation (SC) decoding algorithm is However, the SC decoding algorithm and the improved method of the SC decoding algorithm are essentially serial, which produces a long decoding delay and cannot achieve high throughput, wherein, is the code length of the polar code, and n is a positive integer; the Belief propagation (BP) decoding algorithm, as another important decoding method of polar codes, can effectively reduce the decoding delay by virtue of its natural parallel computing architecture, and has good error performance by iteratively updating and transmitting messages; however, the original BP decoding algorithm needs multiple iterations and uses a complex nonlinear function to calculate the iteration information of each node, and its complexity is , wherein T is the number of iterations.

[0006] Therefore, without losing performance, it is necessary to reduce the complexity of the original BP decoding algorithm for easy hardware implementation; the main way currently adopted is to simplify the complex nonlinear function for calculating the iteration information to reduce the complexity of the original BP decoding, such as the Min-Sum (MS) algorithm and the Improve-MS algorithm, but these algorithms sacrifice certain error performance while reducing complexity.

[0007] The MS algorithm simplifies the complex iterative information calculation formula into a comparison operation, which greatly reduces the complexity, but causes a loss in error rate performance. The Improve-MS algorithm performs piecewise fitting on the complex iterative information calculation formula to reduce the fitting error, so as to reduce the impact on error rate performance while reducing computational complexity. However, the iterative information update formulas used by these methods have a certain fitting error compared with the iterative information update formula of the original BP decoding algorithm, which makes the error rate performance worse. Summary of the Invention

[0008] 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.

[0009] 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 bits of information, 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 , , ,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. 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. in The specific expression is as follows: When x and y satisfy the condition hour, ,in, , , , The specific expression is, ; 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 , .

[0010] 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

[0011] Figure 1 The flowchart illustrates an improved high-performance BP decoding method for polar codes provided by this invention.

[0012] 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.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] 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.

[0017] 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

[0018] 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.

[0019] 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 hour, ,in, , ,when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ;when hour, ; (2) When , .

[0020] 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 bits of information, 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 , , ,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 , .

[0021] 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, where the maximum number of iterations is 50.

[0022] Table 1 shows the running time of different decoding algorithms when the code length is 1024. 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 improved high-performance BP decoding method for polar codes provided by this invention is as follows: Figure 1 As 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, a 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 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 bits of information, 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 , , ,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. 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; Where the iterative information update formula The specific expression depends on the magnitudes of the input variables x and y: When the values ​​of x and y are both small, ; When the values ​​of x or y are large, or when the values ​​of x and y are both large, ; 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 iterative information update formula needs to be determined based on the following criteria. The input values ​​x and y can be large or small: If the values ​​of input variables x and y satisfy the condition Then it is assumed that the values ​​of x and y are both small, and ; If the values ​​of input variables x and y satisfy the condition If x or y is larger, or if both x and y are larger, then it is considered that either x or y is larger. .

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 fitting functions used were exponential, logarithmic, reciprocal, and constant functions. , ; 。 5. The method according to claim 4, characterized in that, functions in The specific expression is: 。

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