Research On Algorithm Of Arbitrary-Length Polar Code

Polar code's performance is superior,and the coding and decoding algorithm has low complexity.It is an excellent coding scheme.When the code length is long enough,the channel capacity limit can be reached.Due to the structure of the polar code,the polar code has a large limitation,that is,the code length must satisfy the power of 2.This limitation affects the role of polar codes in practical applications.In order to solve this problem,this paper discusses the construction method of arbitrary-length polar code.The study found that the puncturing scheme has a large impact on the performance of the polar code and will increase the average complexity of each bit.However,multi-core polar codes are still limited by structure.Although the choice of code length is improved,the code length cannot be set to an arbitrary length,and the decoding algorithm consumes more resources.Therefore,this paper designs a coding scheme that can maintain the excellent performance and low complexity of the polar code,and can break the limitation of the code length of the polar code.This paper proposes a polar code construction method with arbitrary code length.The main research of this paper is the polar code construction method of arbitrary code length.According to the hexadecimal conversion,any positive integer can be decomposed into a number of two n-th power addition forms.As long as the code length of the polar code is decomposed,each item after decomposition is a power of 2 n,which satisfies The code length requirement of the traditional polar code.Based on this,this paper proposes a new method for constructing arbitrary code length polar codes,called step-by-step polar code.It can construct a polar code of arbitrary code length.The step-by-step polar code is composed of sub-polar codes having different code lengths,and the sub-polar code is determined by the decomposition result of the total code length.In order to improve the coding performance,this paper proposes a polarization effect priority algorithm to generate a scheme for combining sub-polar codes.The combined scheme generated by the algorithm can reduce the number of incompletely polarized channels,and can improve the combined performance when the sub-polar code length is short.Then,the construction method of the generation matrix of the step-by-step polar code is given,and the coding and decoding algorithm is given according to the structure of the step-by-step polar code.In addition,in this paper,each f and g operation in decoding is regarded as a basic operation unit,by quantifying the basic operation unit,we prove that the stepwise polar codes have lower decoding complexity than punctured or multi kernel polar codes.When the code length is slightly larger than half of the length of the mother code,the Decoding complexity of the stepwise polar codes is about 50%lower than that of the punctured polar codes.As the code length approaches the mother code length,the difference in Decoding complexity gradually decreases.Decoding complexity of multi-kernel polar codes are lower than that of punctured polar codes,but it is also higher than that of stepwise polar codes.Simulation results show that the proposed codes outperform the conventional punctured polar codes.Compared with the PC-short code,the proposed method has an improvement of 0.1 dB,and compared with the RCPP code,the proposed method obtains a gain of about 0.1-0.4 dB.