Nonbinary Quasi-Cyclic LDPC Cycle Codes with Low-Density Systematic Quasi-Cyclic Generator Matrices

A method for constructing parity-check matrices of non-binary quasi-cyclic LDPC codes

An algorithm for constructing parity-check matrices of nonbinary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of t...

Cyclic and Quasi-Cyclic LDPC Codes on Row and Column Constrained Parity-Check Matrices and Their Trapping Sets

This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descenda...

Design of nonbinary quasi-cyclic low-density parity-check codes by maximising the minimum distance

In this paper, we propose a construction method of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes. The shift offset values of the circulant permutation submatrices are selected not only by maximising the girth but also by maximising the minimum distance upper bound. The proposed method provides a more rational optimisation way than only maximising the girth. Copyright © 2012 Jo...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Quasi-cyclic LDPC codes from difference families

We consider in this paper regular and nearly regular quasi-cyclic low-density paritycheck (LDPC) codes, derived from families of difference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding.