Research On Rate Marching And Encoding Scheme Of Polar Codes

Polar codes,proposed by Arikan,were the first family of error correcting codes that provably achieve the capacity.Polar codes have excellent error-correcting ability and relatively lower coding and decoding complexity.Polar codes with length of N and successive cancelation decoder have the quasi-linear coding and decoding complexity of O（NlogN）.In this paper,based on the coding principle,polar codes were optimized from the aspects of rate matching and relaxing polarization.Firstly,this paper systematically introduced the basic knowledge of polar codes,which was mainly divided into three parts.The first part is the principle of channel polarization,the recursive formula of channel merging and channel splitting was given,and the generation steps of polar codes were explained.In the second part,several common information bits selection methods were introduced,and the application scope and advantages and disadvantages of these methods were described and compared.Thirdly,several decoding methods were given,and their differences in complexity,decoding delay and error correction performance were compared.The encoding method of polar codes determined that the code length and code rate of the original polar codes were not flexible.So,it is necessary to construct the variable code length and rate matching polar codes by puncturing.In this paper,a segmented puncturing method was proposed to construct the rate matching polar codes.The matrix polarization rate was introduced to measure the effect of puncturing on polar codes'error correction performance.The codeword with the largest matrix polarization rate was selected as the optimal puncturing mode.The codeword was segmented,which can effectively reduce the burden of search computation,so that it is possible to find for the optimal puncturing mode by exhaustive search.The simulation results showed that,compared with the traditional puncturing polar codes,the method in this paper can obtain about 0.7dB coding gain when bit error rate is 10^-3.The segmented puncturing method can effectively improve the decoding performance of rate matching polar codes.It is difficult to balance complexity and error correction performance at the same time from decoding method aspect.In order to reduce complexity and maintain the error correction performance at the same time,relaxed polar codes were proposed.The relaxed polar codes reduce the computation complexity in terms of polarization and encoding process,which can fundamentally reduce the complexity without error probability lossing.The original relaxed polar codes were based on 2x2 generation matrix,as 3x3 generation matrix has a better theoretical performance than the 2x2 generation matrix,so applying the3x3 generation matrix to the relaxed polar codes can further improve the performance.Firstly,it was proved that the relaxed polar codes based on 3x3 generation matrix have better error correction performance than the corresponding traditional polar codes.Next,the theoretical bounds of the complexity reduction ratio of different 3x3 generation matrices under infinite code length and finite code length was analyzed.Then,the simulation was executed for the complexity reduction ratio and error correction performance of relaxed polar codes with different 3x3 generation matrices.The results showed that different 3x3 generation matrices are suitable for different polarization and channel condition.Also,relaxed polar codes with the optimal 3x3 generation matrix can reduce the complexity by up to 85.7%.Moreover,the error correction performance of relaxed polar codes with 3x3 generation matrices are better than that with 2x2 generation matrices.