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

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

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...

Efficient encoding for a family of quasi-cyclic LDPC codes

In general, encoding for LDPC codes can be difficult to realize efficiently. This paper presents techniques and architectures for LDPC encoding that are efficient and practical for a particular class of codes. These codes are the irregular partitioned permutation LDPC codes recently introduced by the author at ICC’03, [4]. Since these codes are quasi-cyclic, it is known that a simpler encoding ...

BCRI preprint On a class of quasi-cyclic LDPC codes

Abstract. We study a class of quasi-cyclic LDPC codes. We provide both a Gröbner basis approach, which leads to precise conditions on the code dimension, and a graph theoretic prospective, that lets us guarantee high girth in their Tanner graph. Experimentally, the codes we propose perform no worse than random LDPC codes with their same parameters, which is a significant achievement for algebra...

Computation of Grobner Basis for Systematic Encoding of Generalized Quasi-Cyclic Codes

Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Gröbner basis of modules, there has been no algorithm that computes G...

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...