Analysis of Error Floors of Non-Binary LDPC Codes over MBIOS Channel

TL;DR

This paper analyzes the error floors of non-binary LDPC codes over MBIOS channels, providing conditions for decoding success, and establishing lower bounds for error floors in expurgated ensembles.

Contribution

It introduces a necessary and sufficient condition for decoding success of zigzag cycle codes and derives lower bounds for error floors of non-binary LDPC codes over MBIOS channels.

Findings

Derived a condition for successful decoding of zigzag cycle codes.

Established lower bounds for error floors of expurgated LDPC ensembles.

Analyzed the impact of code expurgation on error floors.

Abstract

In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the belief propagation decoder. We consider an expurgated ensemble of non-binary LDPC codes by using the above necessary and sufficient condition, and hence exhibit lower error floors. Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channel.