关键词: 极化码, 核矩阵, 克罗内克积, 多核构造

Abstract:

As the first channel coding that can be theoretically proven to achieve channel capacity,polar codes are the coding scheme for control channels in 5G enhanced mobile broadband scenarios.Aiming at the limitation of traditional polar codes in constructing the large-dimensional kernel matrix,this paper proposes an improved method of shortening the kernel based on Kronecker multi-kernel construction.The method first selects factor matrices with a large exponent in the process of multi-kernel construction to obtain matrices with a better performance.Then we use the characteristic of the partial distance to shorten the matrix to obtain a kernel matrix with more flexible dimensions and a better performance.In order to solve the problem that partial distances may exceed the corresponding upper bounds in the process of constructing the kernel matrix,this paper proposes an elimination algorithm based on the Hamming distance.According to the characteristic that the partial distance of the matrix row vector will not exceed its Hamming distance,the algorithm reduces the partial distance by reducing the weight of 1 in the row vector.This paper gives the decoding method of the fifth-order kernel matrix,which provides more choices for the construction of multi-kernel polar codes.Experiments show that the shortening method based on column weights can obtain a partial kernel matrix with a larger exponent than the Kronecker multi-kernel construction.The method proposed in this paper is better than other shortening methods with a similar idea in terms of exponent.In terms of decoding,it follows the general structure of traditional polar codes,but has a lower decoding complexity.

Key words: polar codes, kernel matrix, Kronecker product, multi-kernel construction