Statistical Physics of Random Binning

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-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. 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 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.