Research On The Shortening Kernel Matrix Construction Method Of Polar Codes

Polar codes,as the first channel codes theoretically proven to achieve channel capacity,were confirmed as the coding scheme for control channels in 5G mobile broadband scenarios in 2016.It plays an important role in 5G communications.Although polar codes have the advantages of reachable channel capacity and low encoding and decoding complexity,there are still many problems need to be solved in practical applications.The code length of polar codes is fixed to a power of 2,which does not have the arbitrary code length characteristics of coding schemes such as LDPC codes.The puncturing polar codes effectively solves the problem of code length,but it will lose a certain performance and have a large decoding complexity during puncturing.Addressing these problems,the main research contents of this thesis are as follows:(1)A shortening method based on column weights is proposed to construct polar codes of arbitrary code length in this thesis.This method first selects factor matrices with large exponent in the process of multi-kernel construction to ensure better initial performance.Then,the matrix is shortened according to the weight of 1 in the matrix column vector and the characteristics of partial distances to obtain a kernel matrix with more flexible dimensions and better performance.Experiments show that exponent of some matrices obtained by this method is improved about0.02～0.05 compared with multi-kernel construction.The proposed method is exponentially superior to the same type of shortening method,and the larger the partial distance of the last row of the matrix is,the more obvious the advantage of this method will be.It follows the general structure of traditional polar codes in decoding and has lower decoding complexity.Compared with puncturing polar codes,this method reduces the decoding complexity about 60% when constructing polar codes with the same code length.(2)This thesis proposes an elimination algorithm based on Hamming distance.This algorithm effectively solves the problem that the partial distance exceeds the upper bound on the premise of losing the matrix polarization performance as little as possible by utilizing the characteristic that partial distance of the row vector is not higher than its Hamming distance.Then,the loss of polarization performance is reduced by improving the shortening method based on column weights and considering the influence of row vectors on matrix performance more fully.Experiments show that the improved method has better performance when acting on the matrix constructed by Kronecker product multi-kernel.Finally,the corresponding decoding method is given and the feasibility of this method in decoding is verified theoretically.