Optimization of Non Binary Parity Check Coefficients

作     者：Boutillon, Emmanuel 

作者机构：Univ Bretagne CNRS Lab STICC UMR 6285 F-56100 Lorient France 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 (IEEE信息论汇刊)

年 卷 期：2019年第65卷第4期

页      面：2092-2100页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Non-binary parity check non-binary LDPC hamming weight error control code 

摘      要：This paper generalizes the method proposed by Poulliat et al. for the determination of the optimal Galois field coefficients of a non-binary LDPC parity check constraint based on the binary image of the code. Optimal, or almost-optimal, parity check coefficients are given for check degree varying from 4 to 20 and Galois field varying from GF (64) up to GF (1024). For all given sets of coefficients, no codeword of Hamming weight two exists. A reduced complexity algorithm to compute the binary Hamming weight 3 of a parity check is proposed. When the number of sets of coefficients is too high for an exhaustive search and evaluation, a local greedy search is performed. Explicit tables of coefficients are given. The proposed sets of coefficients can effectively replace the random selection of coefficients often used in NB-LDPC construction.