Non binary LDPC codes over the binary erasure channel: density evolution analysis

TL;DR

This paper thoroughly analyzes non-binary LDPC codes over the binary erasure channel, introducing a decoding algorithm and evaluating their asymptotic performance using density evolution, considering graph irregularity and edge label distributions.

Contribution

It introduces a generalized on-the-fly decoding algorithm for non-binary LDPC codes and derives density evolution equations accounting for irregularity and label distributions.

Findings

Decoding algorithm performs on-the-fly as symbols are received.

Density evolution equations incorporate graph irregularity and label distributions.

Asymptotic performance of non-binary LDPC ensembles demonstrated for various label distributions.

Abstract

In this paper we present a thorough analysis of non binary LDPC codes over the binary erasure channel. First, the decoding of non binary LDPC codes is investigated. The proposed algorithm performs on-the-fly decoding, i.e. it starts decoding as soon as the first symbols are received, which generalizes the erasure decoding of binary LDPC codes. Next, we evaluate the asymptotical performance of ensembles of non binary LDPC codes, by using the density evolution method. Density evolution equations are derived by taking into consideration both the irregularity of the bipartite graph and the probability distribution of the graph edge labels. Finally, infinite-length performance of some ensembles of non binary LDPC codes for different edge label distributions are shown.