  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.
