on the girth of tanner (3,7) 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...

Girth of Tanner’s (3, 5) Quasi-Cyclic LDPC Codes

In this paper, the cycles of Tanner’s (3, 5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner’s (3, 5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15-th root of unity of the prime field Fp. By checking the existence of solutio...

Girth-12 Quasi-Cyclic LDPC Codes with Consecutive Lengths

A method to construct girth-12 (3,L) quasi-cyclic lowdensity parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes can be arbitrary integers of the form LP, provided that P is larger than a tight lower bound determined by the maximal element within the exponent matrix of t...

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

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...

on the grobner basis of a family of quasi-cyclic ldpc codes