F_(3)上一类极化码的性质  

Properties of a class of polar codes over F_(3)

作　　者：高俊杰 李秀丽[1] GAO Jun-jie;LI Xiu-li(School of Mathematics&Physics,Qingdao University of Science&Technology,Qingdao 266061,China)

机构地区：[1]青岛科技大学数理学院,山东青岛266061

出　　处：《齐鲁工业大学学报》2022年第6期68-74,共7页Journal of Qilu University of Technology

摘　　要：极化码是一种新型的编码方式,在对称二元输入离散无记忆信道下通过合成与分裂信道会产生极化现象。Arikan在理论上证明了极化码可以达到香农极限。核矩阵决定了信道合成与分裂的效果。研究了有限域F_(3)上的极化率最优的3阶核矩阵B_(N)G_(3)^(n)(B_(N)是一个置换矩阵,n表示n次克罗内克积)。通过编程发现F_(3)上互不等价的极化率最优的核矩阵共计18个。选取了一个特定核矩阵分析并证明了其相关性质。Polar coding is a new method which realizes polarization through channel synthesis and channel splitting in symmetric binary input discrete memoryless channel.Arikan proved that polar codes can reach shannon limit in theory.The effect of channel synthesis and channel splitting are decided by the kernel matrix.The third order kernel matrix B_(N)G_(3)^(n)(B_(N)is studied(B_(N)is a permutation matrix,and n represents the n-th krolecker product)with optimal polarizability on finite field F_(3).Through programming,the results show that there are 18 kernel matrices with optimal polarizability on F_(3)that are not equivalent to each other.A particular kernel matrix is selected to analyze and its related properties are proved.

关 键 词：多元有限域 极化码 核矩阵 巴氏参数 矩阵指数 

分 类 号：TN911.22[电子电信—通信与信息系统]