New fast density evolution method for low density parity-check codes using higher-order statistic

Abstract

Density evolution (DE) is a technique for tracking the distribution of the log likelihood ratio (LLR) messages exchanged between the variable nodes and the check nodes in a bipartite graph. It is widely assumed that these distributions are close to Gaussian. However, in many scenarios, this assumption is not valid, for example, the case that the signal to noise ratio is low, or the degree of variable nodes exceeds a certain threshold. A new (suboptimal) method for DE algorithm in low-density parity-check codes is introduced. We provide a more accurate model for the distribution of message bits (as compared to Gaussian) through matching the first n statistical moments. An iterative message passing algorithm is proposed to compute these moments from the graphical representation of the underlying code. It shown that the proposed algorithm results in an improved estimate of the underlying EXIT chart as compared to using a Gaussian assumption. In this respect, the proposed method achieves a performance very close to that of the best earlier methods, while it offers a much lower complexity.