Performance of Standard Irregular LDPC Codes under Maximum Likelihood Decoding

Ryoji IKEGAYA  Kenta KASAI  Tomoharu SHIBUYA  Kohichi SAKANIWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.7   pp.1432-1443
Publication Date: 2007/07/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.7.1432
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
low-density parity-check (LDPC) code,  maximum-likelihood decoding,  standard irregular LDPC code ensemble,  block error probability,  

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In this paper, we derive an upper bound for the average block error probability of a standard irregular low-density parity-check (LDPC) code ensemble under the maximum-likelihood (ML) decoding. Moreover, we show that the upper bound asymptotically decreases polynomially with the code length. Furthermore, when we consider several regular LDPC code ensembles as special cases of standard irregular ones over an additive white Gaussian noise channel, we numerically show that the signal-to-noise ratio (SNR) thresholds at which the proposed bound converges to zero as the code length tends to infinity are smaller than those for a bound provided by Miller et al.. We also give an example of a standard irregular LDPC code ensemble which has a lower SNR threshold than a given regular LDPC code ensemble.