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.

This paper is concerned with the evaluation of the block error probability of maximum likelihood decoding (MLD) for a block code or a block modulation code over an AWGN channel. It is infeasible to evaluate the block error probability of MLD for a long block code with a large minimum distance by simulation. In this paper, a new evaluation method of the block error probability of MLD by an analytical method combined with simulation with a low-weight sub-trellis diagram is proposed. We show that this proposed method gives a tighter upper bound on the block error probability than the conventional one, and can be applicable to a relatively long block code with a large minimum distance for which conventional simulation is infeasible.

This paper is concerned with the evaluation of the block error probability Pic of a block modulation code for closest coset decoding over an AWGN channel. In most cases, the conventional union bound on Pic for closest coset decoding is loose not only at low signal-to-noise ratios but at relatively high signal-to-noise ratios. In this paper, we introduce a new upper bound on the probability of union of events by using the graph theory and we derive an improved upper bound on Pic for some block modulation codes using closest coset decoding over an AWGN channel. We show that the new bound is better than the conventional union bound especially at relatively high signal-to-noise ratios.