Analysis And Research On The Decoding Algorithms Of Polar Codes

Polar codes,proposed by Arikan in 2008,are the first family of codes that be proved to achieve the Shannon capacity.Because Polar codes have the characteristics of low complexity in encoding and decoding algorithms,no error floor and capacity-achieving,they have become a research hotspot in the field of channel codes.Polar codes can achieve the Shannon capacity when the code length tends to infinity,however for its practical applications,the performance of Polar codes with short and moderate block lengths is not ideal under the SC decoding algorithm.The introduction of the parallel BP decoding algorithm solves the shortcoming of the high latency of the SC decoding algorithm.But in the decoding algorithm of Polar codes,the problems of reducing the complexity of BP decoding algorithm and improving the performance of SC decoding algorithm require further theoretical research.This dissertation focuses on the decoding of Polar codes with the short and moderate block lengths,the major contributions are listed as follows:In order to reduce the complexity of BP decoding algorithm for Polar codes,we present two improved algorithms for Polar codes.First,a method has been proposed to simplify the node update rules in the BP decoding algorithm,which replace the hyperbolic functions with linear approximation functions based on the principle of equal spacing.The complexity of the improved algorithm and BP decoding algorithm is compared and analyzed in detail.The improved algorithm only needs multiplication and addition operations,which can effectively reduce the computational complexity of the algorithm without losing the performance of BP decoding algorithm.Secondly,an improved BP decoding algorithm based on the principle of equal error has been proposed.And the differences between two methods have been compared.Simulation results show that the two improved algorithms can achieve the same performance,and the decoding algorithm based on equal error requires less storage space and better suitable for the case of storage limitation.A modified method has been proposed to improve the performance of the min-sum decoding algorithm.Compared with the min-sum decoding algorithm,the modified min-sum decoding algorithm improves the performance,and can be a better approach to the BP decoding algorithm with little computational cost.The simulation results show that the performance of the improved min-sum decoding algorithm is almost the same as the BP decoding algo-rithm,and better than the min-sum decoding algorithm.And in terms of the computation complexity,the modified min-sum decoding algorithm is lower than the BP decoding algorithm.For solving the problem of stopping iteration in the BP decoding algorithm,an early stopping criteria is proposed for BP decoding algorithm,and the core idea is to use the CRC check to determine whether stop iteration while the iterations have reached the set times 5.When the SNR is greater than 2.5 d B,the iterations of the improved algorithm are 90% lower than that of the BP decoding algorithm in the case of losing a little performance.The improved scheme improves the decoding delay problem of the BP decoding algorithm,which reduces the complexity of the algorithm.Moreover,in order to solve the problem of the performance loss caused by the above early stopping iterative criterion,a BP decoding algorithm with enhanced performance has been proposed base on the early stopping criterion.In the improved algorithm,in the leftmost end of the factor graph,when the LLR values of the left messages of the information bit nodes are larger than the threshold value,the LLR value of right messages of the nodes are set to the LLR value of the frozen bits while the symbol remains unchanged.The algorithm not only reduces the iterations of the algorithm,but also improves the decoding performance of BP decoding algorithm.According to the problem of candidate paths selection in CRC-SCL decoding algorithm,an improved CRC-SCL decoding algorithm has been proposed.In each layer of the improved CRC-SCL decoding algorithm,the best L candidate paths are selected,and the other paths to meet the condition also joined in the candidate paths,which increases the probability that the correct path is selected.The simulation results show that the improved CRC-SCL decoding algorithm increases the computational complexity of some nodes,but its decoding performance is better than CRC-SCL decoding algorithm.