We investigate the behavior of iteratively decoded low-density parity-check (LDPC) codes over the binary erasure channel in the so-called ldquowaterfall region.rdquo We show that the performance curves in this region follow a simple scaling law. We conjecture that essentially the same scaling behavior applies in a much more general setting and we provide some empirical evidence to support this conjecture. The scaling law, together with the error floor expressions developed previously, can be used for a fast finite-length optimization.

We show that the finite-length scaling parameters for irregular LDPC codes when used over the binary erasure channel can be computed without resorting to "covariance evolution". We provide simple expressions that can be evaluated using solely the degree distributions and the characteristics of the fixed point of density evolution

We investigate the finite-length scaling methodology for irregular LDPC code ensembles when transmission takes place over the binary erasure channel (BEC). We first show how the necessary computations, namely the covariance evolution and the computation of the finite-length shift, can be accomplished in the irregular case. We then investigate how the obtained approximation can be used to predict the performance of irregular code ensembles and to optimize the degree distributions for finite-length codes.

The behavior of iteratively decoded low-density parity-check (LDPC) codes over the binary erasure channel in the so-called "waterfall region" is investigated and shows that the performance curves in this region follow a very basic scaling law. This scaling law, combined with previously known expressions for the error floor, yields a promising direction for analyzing the performance of irregular LDPC codes of practical lengths.