On the Construction of Quasi-Cyclic Low-Density Parity-Check Codes Based on Girth

Toshihiko OKAMURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.9   pp.2432-2439
Publication Date: 2004/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
low-density parity-check code,  quasi-cyclic code,  Tanner graph,  girth,  array code,  irregular code,  

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In this paper, we propose a method for constructing quasi-cyclic low-density parity-check codes randomly using cyclic shift submatrices on the basis of the girth of the Tanner graphs of these codes. We consider (3, K)-regular codes and first derive the necessary and sufficient conditions for weight-4 and weight-6 codewords to exist. On the basis of these conditions, it is possible to estimate the probability that a random method will generate a (3, K)-regular code with a minimum distance less than or equal to 6, and the proposed method is shown to offer a lower probability than does conventional random construction. Simulation results also show that it is capable of generating good codes both regular and irregular.