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.
基金
the Research Council of Shahrekord University
作者简介
The corresponding author:F.Abedi,received the B.S.&M.S.degrees in Applied Mathematics in 2012&2014,respectively,from University of Isfahan,Isfahan,Iran,and she is now pursuing the Ph.D degree in Mathematics(Coding Theory)in Shahrekord University,Shahrekord,Iran,under Supervisor of Dr.Mohammad Gholami.Her research interest includes algebraic coding theory,LDPC codes and algebraic decoding algorithms.email:gholami-m@sci.sku.ac.ir;M.Gholami,has graduated in Mathematics in 2003 with honors from the Sharif University of Technology,Tehran,Iran,and the Ph.D degree in Mathematics(Information and Coding Theory)in 2009 form Isfahan University of Technology,Isfahan,Iran.Since September 1998 he has been with the Department of Mathematical Sciences at Shahrekord University,Shahrekord,Iran,where he was received the grade of Associate Professor from October 2015.
