Statistical Physics of Random Binning

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