On Gaussian Approximation for Density Evolution of Low-Density Parity-Check Codes

This paper is concerned with density evolution for iterative decoding of low-density parity-check (LDPC) codes. We first study the problem of density evolution computation for regular LDPC codes. For this, we propose a simple computational algorithm based on the ergodicity theory. This method is shown to match very well with explicit calculations of density functions. The second problem we study is about the approach of Gaussian approximation to density evolution. We point out that it is inappropriate to use the mean of the density only to model the iterative decoding process. Instead, both the mean and variance are needed for Gaussian approximation. Finally, we consider the problem of density evolution for irregular LDPC codes. For this, we extend the density evolution algorithm for regular LDPC codes to irregular LDPC codes. We then illustrate that Gaussian approximation is also valid provided that the degree distributions are not wide. A dynamic model is also presented based on Gaussian approximation.