TITLE:
On the Construction of the Kernel Matrix by Primitive BCH Codes for Polar Codes
AUTHORS:
Liping Lin
KEYWORDS:
Polar Code, Kernel Matrix, Matrix Interception, Partial Distance, Exponent, Scaling Exponent
JOURNAL NAME:
Communications and Network,
Vol.14 No.1,
January
21,
2022
ABSTRACT: The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2n-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2n-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.