New Density Evolution Approximation for LDPC and Multi-Edge Type LDPC Codes

TL;DR

This paper introduces a new density evolution approximation method for LDPC and MET-LDPC codes that improves accuracy and reduces computational time for code threshold estimation, especially at low rates and with punctured nodes.

Contribution

A novel hybrid density evolution approximation combining full density evolution and Gaussian assumptions, enhancing accuracy and efficiency in code threshold analysis.

Findings

The new method outperforms existing Gaussian approximations in accuracy.

It significantly reduces computational time for threshold evaluation.

The approach is particularly effective at low code rates and with punctured nodes.

Abstract

This paper considers density evolution for lowdensity parity-check (LDPC) and multi-edge type low-density parity-check (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three singleparameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared to full density evolution thereby making it more suitable for code design.