Statistical mechanics of sensing and communications: Insights and techniques

Abstract

In this article we review a basic model for analysis of large sensor networks from the point of view of collective estimation under bandwidth constraints. We compare different sensing aggregation levels as alternative 'strategies' for collective estimation: moderate aggregation from a moderate number of sensors for which communication bandwidth is enough that data encoding can be reversible, and large scale aggregation from very many sensors - in which case communication bandwidth constraints require the use of nonreversible encoding. We show the non-trivial trade-off between sensing quality, which can be increased by increasing the number of sensors, and communication quality under bandwidth constraints, which decreases if the number of sensors is too large. From a practical standpoint, we verify that such a trade-off exists in constructively defined communications schemes. We introduce a probabilistic encoding scheme and define rate distortion models that are suitable for analysis of the large network limit. Our description shows that the methods and ideas from statistical physics can play an important role in formulating effective models for such schemes.