The Dynamic Phase Transition for Decoding Algorithms

TL;DR

This paper explores the decoding process of advanced error-correcting codes through statistical physics models, revealing intrinsic dynamic phase transitions that influence algorithm performance.

Contribution

It introduces a novel analysis linking decoding algorithms to phase transitions in diluted mean-field spin glasses, providing new insights into their behavior.

Findings

Decoding algorithms exhibit a dynamic phase transition.

Intrinsic features of decoding are characterized by spin glass models.

Analysis explains performance limits of iterative decoding.

Abstract

The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of diluted mean-field spin glasses, both from the static and from the dynamic points of view. We analyze the behavior of decoding algorithms using the mapping onto statistical-physics models. This allows to understand the intrinsic (i.e. algorithm independent) features of this behavior.