Design of LDPC Codes Robust to Noisy Message-Passing Decoding

TL;DR

This paper analyzes the impact of internal decoder noise on LDPC code performance over AWGN channels, using density evolution and EXIT charts to design codes that are robust against such noise.

Contribution

It introduces a Gaussian approximation-based density evolution method for noisy LDPC decoders and proposes a design approach for robust irregular LDPC codes.

Findings

Quantifies performance loss due to internal decoder noise.

Demonstrates that designed codes can partially compensate for performance degradation.

Abstract

We address noisy message-passing decoding of lowdensity parity-check (LDPC) codes over additive white Gaussian noise channels. Message-passing decoders in which certain processing units iteratively exchange messages are common for decoding LDPC codes. The exchanged messages are in general subject to internal noise in hardware implementation of these decoders. We model the internal decoder noise as additive white Gaussian noise (AWGN) degrading exchanged messages. Using Gaussian approximation of the exchanged messages, we perform a two-dimensional density evolution analysis for the noisy LDPC decoder. This makes it possible to track both the mean, and the variance of the exchanged message densities, and hence, to quantify the threshold of the LDPC code in the presence of internal decoder noise. The numerical and simulation results are presented that quantify the performance loss due to the internal decoder noise. To partially compensate this performance loss, we propose a simple method, based on EXIT chart analysis, to design robust irregular LDPC codes. The simulation results indicate that the designed codes can indeed compensate part of the performance loss due to the internal decoder noise.