Statistical physics of random binning

TL;DR

This paper applies statistical physics models to analyze the behavior of random binning in Slepian-Wolf coding, revealing phase transitions and deriving the exact error exponent for finite-temperature decoding.

Contribution

It introduces the random dilution model as an analogy for random binning, characterizes phase transitions, and derives the exact random coding exponent for finite-temperature Slepian-Wolf decoding.

Findings

Phase transitions in finite-temperature Slepian-Wolf decoding characterized.

Exact random coding exponent for BER derived as a function of rate and temperature.

Analogies established between random binning and statistical mechanical models.

Abstract

We consider the model of random binning and finite-temperature decoding for Slepian-Wolf codes, from a statistical-mechanical perspective. While ordinary random channel coding is intimately related to the random energy model (REM) - a statistical-mechanical model of disordered magnetic materials, it turns out that random binning (for Slepian-Wolf coding) is analogous to another, related statistical mechanical model of strong disorder, which we call the random dilution model (RDM). We use the latter analogy to characterize phase transitions pertaining to finite- temperature Slepian-Wolf decoding, which are somewhat similar, but not identical, to those of finite-temperature channel decoding. We then provide the exact random coding exponent of the bit error rate (BER) as a function of the coding rate and the decoding temperature, and discuss its properties. Finally, a few modifications and extensions of our results are outlined and discussed.