Some Explicit Constructions of Type-Ⅱ,Ⅲ,Ⅳ,Ⅴ QC-LDPC Codes with Girth 6  

作　　者：Farzaneh Abedi Mohammad Gholami 

机构地区：[1]Department of Mathematics,Shahrekord University,P.O.Box 88186-34141,Shahrekord,Iran [2]School of Computer Sciences,Institute for Research in Fundamental Sciences(IPM),P.O.Box 19395-5746,Tehran,Iran

出　　处：《China Communications》2020年第5期89-109,共21页中国通信（英文版）

基　　金：the Research Council of Shahrekord University

摘　　要：Multi-type quasi-cyclic(QC) low-density parity-check(LDPC) codes can be considered as multiple-edge protograph QC-LDPC codes having some advantages in the minimum Hamming distance bound over single-edge protograph codes or type-Ⅰ QC-LDPC codes when the base matrices have the same size. In this paper, we investigate a class of multi-type QC-LDPC codes whose parity-check matrices contain just one blockrow of circulants and we obtain the generator matrix of such codes in general form. Using the permutation arrays and defining injection arrays, we present a new approach to construct a class of high-rate type-Ⅰ QC-LDPC codes with girth 6 from the constructed 4-cycle free multi-type QC-LDPC codes. In continue, for 2 ≤ w≤6, some type-w QC-LDPC codes with girth 6 are constructed explicitly such that the constructed codes are flexible in terms of rate and length. To the best of our knowledge, for w = 5,6, this is the first paper which deals with the explicit construction of type-w QC-LDPC codes with girth 6 and high rates. Moreover, for w = 3, 4, the constructed type-w QC-LDPC codes have better(6,8)-cycle multiplicities than the codes with minimum achievable length recently constructed by cyclic difference families(CDFs). Simulation results show that the binary and non-binary constructed codes outperform the constituent underlying QC-LDPC codes.

关 键 词：QC-LDPC codes permutation arrays GIRTH explicit constructions 

分 类 号：TN911.22[电子电信—通信与信息系统]