Research On Belief Propagation Decoding Algorithm Of Polar Codes Based On Permutation Factor Graph

Among the existing channel coding techniques,polar code is the only one which has been proved theoretically to be able to reach the Shannon limit,and its coding and decoding complexity is low,so it has very important research significance.Polarization theory shows that the Shannon limit of channel capacity can be reached as the code length tends to infinity.Due to incomplete channel polarization under finite code length,the performance of polar code decoding algorithm will be poor in practical application.Successive Cancellation(SC)decoding algorithms are known for low complexity,but have problems such as large delay and low throughput among traditional polar code decoding algorithms.However,Belief Propagation(BP)decoding algorithm is a parallel structure with small delay and high throughput.Therefore,Therefore,BP decoding algorithm has great application value.This paper mainly studies BP decoding based on permutation factor graph and its improved algorithm.The specific work is summarized as follows:1.The polarization theory of polar codes and the process of encoding and decoding are studied,and the decoding algorithms of BP,SC,and Serial Cancellation List(SCL)are simulated.The results show that SCL decoding algorithm is superior to BP decoding algorithm,and BP decoding algorithm is superior to SC decoding algorithm.2.An improved Belief Propagation List(BPL)algorithm based on Cyclic Redundancy Check(CRC)is proposed.The algorithm realizes a method that selects a good code word set by using CRC check,and outputs the code word precisely by calculating Euclidean distance.The simulation results show that for polar codes with code length of 1024 and code rate of 0.5,the proposed improved BPL algorithm based on CRC can effectively improve the performance of the BPL algorithm.Compared with the traditional BPL algorithm,the proposed BPL algorithm based on CRC has a SNR gain of about 0.31d B at frame error rate of 10^-3.3.An early termination BPL decoding algorithm based on segmentation is proposed.This algorithm can effectively adjust the balance between performance and complexity of BPL decoding algorithm by estimating and screening factor graph in advance,and flexibly selecting calibration strategy according to setting different threshold values.The early termination BPL decoding algorithm based on segmentation has achieved good results in both improving performance and reducing complexity.Simulation results show that the code length is 256,code rate of 0.5 polar code,the bit error rate of 10^-3,Early Termination BPL Decoding Algorithm Based on segmentation than single CRC aided BPL decoding algorithm is about 0.4 d B SNR gain.and When the SNR is 2d B,the average iteration times of the Early Termination BPL Decoding Algorithm Based on segmentation are 33.92 times less than the average iteration times of single CRC aided BPL decoding algorithm.