Algebraic Constructions of High Performance and Efficiently Encodable Non-Binary Quasi-Cyclic LDPC Codes

Newly Designed Quasi-Cyclic Low Density Parity Check Codes

This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight which has cut down hardware implementation cost and complexity as compared to the connection of individual columns and rows. The construction of newly obtained codes gives a class of efficiently encodable quasi-cyclic LDPC codes.

An Unnoticed Strong Connection Between Algebraic-Based and Protograph-Based LDPC Codes, Part II: Nonbinary Case and Code Construction

This paper is the second part of a series of two papers on the investigation of the connection between two methods for constructing LDPC codes, namely the superposition and the protograph-based methods. In the first part, by taking the graph point of view, we established a strong connection between these two construction methods and showed that, in the binary case, the protograph-based construc...

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 Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Design of LDPC Codes: A Survey and New Results

This survey paper provides fundamentals in the design of LDPC codes. To provide a target for the code designer, we first summarize the EXIT chart technique for determining (near-)optimal degree distributions for LDPC code ensembles. We also demonstrate the simplicity of representing codes by protographs and how this naturally leads to quasi-cyclic LDPC codes. The EXIT chart technique is then ex...