Graphical Models and Statistical Mechanics in Communications and Storage Applications

Опубликовано 7 сентября 2016, 17:02

Many real-world systems in communications (e.g. cellular networks) and storage (e.g. magnetic recording devices) can be modeled as two dimensional grids. Each grid point contains the desired local information, which is corrupted by interference from neighboring grid points and by ambient noise. In spite of their widespread use, many properties of such systems are currently unknown. One of these important properties is the estimation problem, i.e, accurately restoring information from a set of contaminated reads from the system. Another open question is calculating the information capacity of such systems. We present a formulation which allows addressing these questions in a rigorous manner, based on Graphical Models and Statistical Mechanics. At the heart of our approach is a mapping of the system to an undirected graphical model, and inferring its marginal probabilities using generalized belief propagation (GBP). We then analyze the achievable Shannon-theoretic information rates using two independent approaches, either via the Shannon-McMillan-Breiman theorem, or via the recently derived Guo-Shamai-Verdu theorem. Our experimental study, which is based on common cellular networks and magnetic recording devices, demonstrates that for nontrivial systems, the performance of this fully tractable GBP inference engine is almost identical to optimal performance. It also enables a practically accurate simulation-based estimate of the information rate. Rationalization of this excellent performance of GBP in these settings is addressed. Based on a joint work with Ori Shental (UCSD, Qualcomm), Shlomo Shamai (Technion, Israel), Ido Kanter (Bar-Ilan U., Israel), Anthony Weiss (Tel-Aviv U., Israel) and Yair Weiss (Hebrew U., Israel).