Statistical Physics of Random Binning

DOI10.1109/TIT.2015.2412112zbMATH Open1359.94510arXiv1411.3857OpenAlexW2169693845MaRDI QIDQ2978618

Publication date: 28 April 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1411.3857

Mathematics Subject Classification ID

Applications of statistics to physics (62P35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Information theory (general) (94A15) Channel models (including quantum) in information and communication theory (94A40)