Irregular Low-Density Parity-Check Code Design Based on Euclidean Geometries

Wataru MATSUMOTO  Weigang XU  Hideki IMAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.7   pp.1820-1834
Publication Date: 2003/07/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Euclidean geometry,  low-density parity-check code,  irregular LDPC code,  

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We propose a scheme for the design of irregular low-density parity-check (LDPC) codes based on Euclidian Geometry using Latin square matrices of random sequence. Our scheme is a deterministic method that allows the easy design of good irregular LDPC codes for any code rate and degree distribution. We optimize the LDPC codes using the Gaussian approximation method. A Euclidean Geometry LDPC code (EG-LDPC) is used as the basis for the construction of an irregular LDPC code. The base EG-LDPC code is extended by splitting rows and columns using a table of Latin square matrices of random sequence to determine the edges along which to split. We provide simulation results for codes constructed in this manner evaluated in terms of bit error rate (BER) performance in AWGN channels. We believe that our scheme is superior in terms of computational requirements and resulting BER performance in comparison to creation of irregular LDPC codes by means of random construction using a search algorithm to exclude cycles of length four.