Error Correction Capability of Column-Weight-Three LDPC Codes: Part II

TL;DR

This paper investigates how the girth of Tanner graphs influences the error correction ability of column-weight-three LDPC codes, showing that Gallager A can correct nearly half the girth minus one errors within half the girth iterations.

Contribution

It establishes a direct relationship between girth and error correction capability for column-weight-three LDPC codes using Gallager A decoding.

Findings

Gallager A corrects g/2-1 errors in g/2 iterations for girth g ≥ 10

Error correction capability scales with the girth of the Tanner graph

Provides theoretical bounds on error correction for specific girth values

Abstract

The relation between the girth and the error correction capability of column-weight-three LDPC codes is investigated. Specifically, it is shown that the Gallager A algorithm can correct $g/2-1$ errors in $g/2$ iterations on a Tanner graph of girth $g \geq 10$.