Regular Quasi Cyclic Low Density Parity Check Codes with Girth 8 from Elementary Number Theory

作     者：He Guofeng Li Xiangxue Li Qiang Zhou Zhiheng Zheng Dong 

作者机构：School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Shanghai 200240 P. R. China Hangzhou Key Lab of E-business and Information Security Hangzhou Normal University Hangzhou 310036 P. R. China Department of Computer Science and Technology East China Normal University Shanghai 200241 P. R. China 

出 版 物：《China Communications》 (中国通信（英文版）)

年 卷 期：2012年第9卷第4期

页      面：80-88页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 070104[理学-应用数学] 0802[工学-机械工程] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：supported by the National Natural Science Foundation of China under Grants No.61172085 No.61103221 No.61133014 No.11061130539 and No.61021004 

主　　题：quasi-cyclic LDPC code error floor Shannon limit number theory 

摘      要：This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number *** the column weight,we determine the shift values of the circulant permutation matrices via arithmetic *** proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and *** results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.