Research On Encoding And Decoding And Performance Evaluation For Polar Codes

Scholars have been studying encoding and decoding schemes that can achieve the channel capacity in theory since the development of channel coding.Polar codes are a coding scheme that is capable of achieving the symmetric capacity of binary-input discrete memoryless channels.The codes are also a coding scheme used in the control channel of 5G communications.Polar codes originally introduced are non-systematic polar codes(NSPCs).Polar codes are susceptible to error propagation under successive cancellation(SC)decoding,and the performance of the codes are disappointing at short or moderate block lengths.With the appearance of polar codes based on 3×3 kernel matrix and the proposal of the corresponding construction method,the limitation on the code length type N=2n is broken.However,the inequality of code length and uncertainty of distance spectrum performance analysis bring great inconvenience to the performance analysis of polar codes with different code length types.We started with these two aspects and studied the coding construction and its theory of polar codes.Simulation analysis was conducted for the influence of various encoding schemes and decoding schemes on the performance of polar codes.First of all,the concrete function and internal mechanism of the permutation matrix were analyzed in the generator matrix of polar codes.Then,we provided the specific form of the matrix and inherent arrangement law of target matrix.The coding methods,such as non-systematically polar coding,systematically polar coding and multidimensional kernel matrix coding,are studied.Then,based on the coding methods,the influence of the relevant parameters on SC decoding algorithm and its corresponding improved algorithms and auxiliary algorithms of polar codes were analyzed by simulation.In the case of different code length types,the performance of systematic polar codes(SPCs)based on l×l multidimensional kernel matrix was studied.The performance difference of SPCs and NSPCs was analyzed systematically.The simulation results show that SPCs have better performance in bit error rate(BER)than NSPCs while they have the same frame error rate(FER)performance.Finally,a method of performance evaluation for polar codes was proposed.According to CLAD,the method can be applied for the performance comparison of polar codes based on 2×2 kernel matrix and l×l multidimensional kernel matrix.The specific implementation process of this method was presented in this paper.Simulation results show that the method can effectively evaluate the performance of polar codes with different code length types when CLAD is large enough.