Construction of High-Rate Regular Quasi-Cyclic LDPC Codes Based on Cyclic Difference Families

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.

Quasi-cyclic LDPC codes with high girth

The LDPC codes are codes that approach optimal decoding performances, with an acceptable decoding computational cost ([1, 2, 3]). In this paper we present a class of quasi-cyclic LDPC codes and we show that we are able to guarantee some relevant properties of the codes. Experimentally, their decoding performance is comparable with the performance obtained by random LDPC codes. Traditionally, co...

on the girth of tanner (3,7) quasi-cyclic ldpc codes

‎s‎. ‎kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (qc) low-density parity-check (ldpc)‎ ‎codes‎, ‎i.e‎. ‎tanner $(3,5)$ of length $5p$‎, ‎where $p$ is a prime of‎ ‎the form $15m+1$‎. ‎in this paper‎, ‎by extension this method to‎ ‎tanner $(3,7)$ codes of length $7p$‎, ‎where $p$ is a prime of the‎ ‎form $21m‎+ ‎1$‎, ‎the girth values of tanner $(3,7...

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

Quasi Cyclic LDPC Codes Based on Finite Set Systems

A finite set system (FSS) is a pair (V,B) where V is a finite set whose members are called points, equipped with a finite collection of its subsets B whose members are called blocks. In this paper, finite set systems are used to define a class of Quasi-cyclic lowdensity parity-check (LDPC) codes, called FSS codes, such that the constructed codes possess large girth and arbitrary column-weight d...