On the guaranteed error correction capability of LDPC codes

TL;DR

This paper analyzes how the girth of LDPC codes influences their guaranteed error correction ability under bit flipping algorithms, providing bounds based on graph expansion and trapping sets.

Contribution

It establishes bounds on error correction capability of LDPC codes by linking girth, expansion properties, and trapping sets, advancing understanding of code performance guarantees.

Findings

Lower bound on variable nodes expanding by at least 3γ/4

Upper bound on correction capability via trapping sets

Relation between girth and error correction performance

Abstract

We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable nodes which expand by a factor of at least $3 \gamma/4$ is found based on the Moore bound. An upper bound on the guaranteed correction capability is established by studying the sizes of smallest possible trapping sets.