F_(3)上极化码的核矩阵

Kernel Matrices of Polar Codes over F_(3)

极化码是由Arikan引入的一种新型编码方式。该码在低复杂度的串行相消译码策略下,能够达到任意对称二进制输入离散无记忆信道的信道容量。不同于单一的2阶核矩阵,3阶核矩阵可以采取多种不同的形式,在极化率与2阶极化率相同的情况下,它具有更好的可靠性。研究了F_(3)上3阶核矩阵的构造原理、构造过程及选取最优核矩阵的标准。

Polar code is a new coding method introduced by Arikan.This kind of codes can achieve the channel capacity of any symmetric binary input discrete memoryless channel under the low complexity serial elimination decoding strategy.Unlike the second order matrix with single form,the third order kernel matrix can take many different forms,and it has better reliability when the polarization rate is the same as the second order's.In this paper,the construction principle,construction process and criterion of selecting optimal kernel matrix of the third order kernel matrix over F_(3)are studied.