Survey propagation at finite temperature: application to a Sourlas code as a toy model

TL;DR

This paper extends survey propagation to finite temperatures and applies it to decoding a Sourlas code, showing improved accuracy over belief propagation near the Nishimori temperature.

Contribution

It introduces a finite temperature generalization of survey propagation and demonstrates its effectiveness for decoding Sourlas codes where other methods struggle.

Findings

Finite temperature survey propagation shifts the dynamical transition to higher noise levels.

The method provides accurate decoding results where belief propagation fails.

It confirms the potential of survey propagation for finite temperature decoding in coding theory.

Abstract

In this paper we investigate a finite temperature generalization of survey propagation, by applying it to the problem of finite temperature decoding of a biased finite connectivity Sourlas code for temperatures lower than the Nishimori temperature. We observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation, as suggested recently by Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state.