Automorphism Ensemble Decoding of Quasi-Cyclic LDPC Codes by Breaking Graph Symmetries

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 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...

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.

An Efficient Encoding-Decoding of Large Girth LDPC Codes Based on Quasi-Cyclic

In this paper, we propose a novel method for constructing quasi-cyclic low-density parity check (QC-LDPC) codes based row division method which can guarantee a concentrated node degree distribution with large girth. The main advantage is that large girth QC-LDPC codes can be easily constructed with a variety of block lengths and rates. Simulation results show that the proposed codes perform sig...