Mori, R. and Tanaka, T. (2010) Channel Polarization on q-ary Discrete Memoryless Channels by Arbitrary Kernels. Proceedings of 2010 IEEE International Symposium on Information Theory, Austin, 13-18 June 2010, 894-898.
https://doi.org/10.1109/ISIT.2010.5513568

has been cited by the following article:

• 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.