极化码四阶核矩阵的构造

doi:10.3976/j.issn.1002-4026.2021.03.014

山东科学 ›› 2021, Vol. 34 ›› Issue (3): 100-108.doi: 10.3976/j.issn.1002-4026.2021.03.014

极化码四阶核矩阵的构造

马奎明，李秀丽*

青岛科技大学数理学院，山东青岛 266061

收稿日期:2020-09-16 出版日期:2021-06-20 发布日期:2021-06-07
通信作者: 李秀丽，女，博士，研究方向为组合设计与编码理论。Tel：15865528506，E-mail: lixiuli2007@aliyun.com
作者简介:马奎明（1995—），男，硕士研究生，研究方向为组合设计与编码理论。E-mail:qdkd2018@163.com
基金资助:
国家自然科学基金(11671235，11801295)

Construction of fourth-order kernel matrix of polar code

MA Kui-ming, LI Xiu-li*

College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

Received:2020-09-16 Online:2021-06-20 Published:2021-06-07

摘要/Abstract

摘要： 极化码是目前唯一被证明理论上可达到香农极限的线性纠错信道编码。在已有的极化码二、三阶核矩阵研究的基础上，提出了最优四阶核矩阵的构造标准：主对角线全为1 且最后一行“1”的个数为4，并由此给出了符合标准的全部矩阵。不同于只有单一线性形式的二阶核矩阵，四阶核矩阵可以采取多种不同的形式，这一点使得极化码在构造时能够有更多的选择。然后以核矩阵为例，详细介绍了信道极化原理。最后总结了利用给定任意维数核矩阵构建特定块长度的极化码的步骤。

关键词: 极化码, 核矩阵, 信道编码, 极化率, 递归结构

Abstract: Polar code is the only linear error-correcting channel code that has been proved theoretically to reach the Shannon Limit. Herein, on the basis of the existing studies on the second and third-order kernel matrices of polar codes, the construction criteria of an optimal fourth-order kernel matrix are proposed: the main diagonals are 1, the number of “1” in the last line is 4, and all the matrices conforming to the abovementioned criteria are determined. Unlike the second-order kernel matrix, which only exhibits a single linear form, the fourth-order kernel matrix can take several forms, providing the polarization codes with more options in the construction. Then, taking the kernel matrix as an example, the channel polarization principle is introduced in detail. Finally, the steps for constructing a polar code having a specific block length with a given kernel matrix of any dimension are summarized.

Key words: polar code, kernel matrix, channel coding; polarizability, recursive structure

中图分类号:

TN911.22

马奎明, 李秀丽. 极化码四阶核矩阵的构造[J]. 山东科学, 2021, 34(3): 100-108.

MA Kui-ming, LI Xiu-li. Construction of fourth-order kernel matrix of polar code[J]. Shandong Science, 2021, 34(3): 100-108.

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极化码四阶核矩阵的构造

Construction of fourth-order kernel matrix of polar code

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