Survey propagation for the cascading Sourlas code

TL;DR

This paper explores how survey propagation, inspired by statistical physics, enhances decoding of sparse error-correcting codes, outperforming belief propagation especially at high connectivity, with potential further improvements via replica symmetry breaking.

Contribution

It establishes the connection between belief propagation and survey propagation, demonstrating the latter's superiority in decoding performance for the Sourlas code.

Findings

Survey propagation outperforms belief propagation at high connectivity.

Time averaged belief propagation is linked to a specific survey propagation.

Second level of replica symmetry breaking may offer further improvements.

Abstract

We investigate how insights from statistical physics, namely survey propagation, can improve decoding of a particular class of sparse error correcting codes. We show that a recently proposed algorithm, time averaged belief propagation, is in fact intimately linked to a specific survey propagation for which Parisi's replica symmetry breaking parameter is set to zero, and that the latter is always superior to belief propagation in the high connectivity limit. We briefly look at further improvements available by going to the second level of replica symmetry breaking.