Extended Non-Binary Low-Density Parity-Check Codes over Erasure Channels

TL;DR

This paper introduces a flexible method for generating extra redundant bits in non-binary LDPC codes, enhancing decoding adaptability over erasure channels without significant complexity increase.

Contribution

It proposes a novel approach to extend non-binary LDPC codes with redundant bits, maintaining decoder compatibility and optimizing for erasure channels using density evolution.

Findings

Redundant bits improve decoding flexibility.

Decoder remains unchanged regardless of redundancy level.

Optimized extended codes perform well over erasure channels.

Abstract

Based on the extended binary image of non-binary LDPC codes, we propose a method for generating extra redundant bits, such as to decreases the coding rate of a mother code. The proposed method allows for using the same decoder, regardless of how many extra redundant bits have been produced, which considerably increases the flexibility of the system without significantly increasing its complexity. Extended codes are also optimized for the binary erasure channel, by using density evolution methods. Nevertheless, the results presented in this paper can easily be extrapolated to more general channel models.