Enhancing Binary Images of Non-Binary LDPC Codes

TL;DR

This paper explains why non-binary LDPC codes outperform their binary images over erasure channels and proposes a method to improve binary image decoding by removing stopping sets, achieving performance close to the original codes.

Contribution

It introduces a technique to identify and add redundant parity-checks to binary images of non-binary LDPC codes, reducing stopping sets and enhancing decoding performance.

Findings

Redundant parity-checks improve binary image decoding performance.

Binary image decoding has higher complexity but worse performance without modifications.

Proposed method achieves performance comparable to original non-binary codes.

Abstract

We investigate the reasons behind the superior performance of belief propagation decoding of non-binary LDPC codes over their binary images when the transmission occurs over the binary erasure channel. We show that although decoding over the binary image has lower complexity, it has worse performance owing to its larger number of stopping sets relative to the original non-binary code. We propose a method to find redundant parity-checks of the binary image that eliminate these additional stopping sets, so that we achieve performance comparable to that of the original non-binary LDPC code with lower decoding complexity.