Reweighted LP Decoding for LDPC Codes

TL;DR

This paper presents a reweighted linear programming decoding algorithm for LDPC codes that improves theoretical guarantees and empirical performance with minimal additional computational cost.

Contribution

It introduces a post-processing reweighting step to the existing LP decoding method, enhancing decoding thresholds and practical performance.

Findings

Improved provable threshold guarantees for certain LDPC ensembles.

Significant empirical performance gains over standard LP decoding.

Minimal additional computational complexity required.

Abstract

We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original LP decoder output. Our analysis shows that for some LDPC ensembles we can improve the provable threshold guarantees compared to standard LP decoding. We also show significant empirical performance gains for the reweighted LP decoding algorithm with very small additional computational complexity.