Elements of information theory
Elements of information theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes
IEEE Transactions on Information Theory
Asymptotic enumeration methods for analyzing LDPC codes
IEEE Transactions on Information Theory
Weight Distribution of Low-Density Parity-Check Codes
IEEE Transactions on Information Theory
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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.