Wireless Ad-Hoc Networks: From Probability to Physics via Information Theory

SPEAKER: Professor Massimo Franceschetti,
University of California, San DiegoABSTRACT: In this interdisciplinary talk we consider the problem of determining the information capacity of a network of wireless transmitters and receivers and try to draw some non-trivial connections between spatial stochastic processes, physics, and information theory.We present the following main result of statistical physics flavor: By distributing uniformly at random an order of n nodes wishing to establish pair-wise independent communications inside a domain of size of the order of n, the per-node information rate must follow an inverse square-root of n law, as n tends to infinity.The above claim originally due --in slightly different form-- to Gupta and Kumar (2000), requires both the construction of a network
operation scheme that achieves the required rate, and an information-theoretic proof of the optimality of such a scheme, at least in the scaling limit sense.We present a scheme due to Franceschetti, Dousse, Tse, and Thiran (2007) which relies on the theory of percolation and achieves the
inverse square-root of n law. Then, departing from the traditional information-theoretic approach of postulating fading channel and path loss models, we apply directly Maxwell's physics of wave propagation in conjunction to Shannon's theory of information, to obtain the "natural" upper bound on the scaling limit of the per-node rate and show that the inverse square-root of n bound is tight. This is a recent result of Franceschetti, Migliore, and Minero (2007).The conclusion is that claims (abundant in the literature) of surpassing the inverse square-root of n law, are artifacts of unrealistic channel modeling assumptions that hide the natural spatial constraints revealed by the Maxwell-Shannon approach.Host: Prof. Urbashi Mitra, ubli@usc.edu

Location: Hughes Aircraft Electrical Engineering Center (EEB) - 248

Audiences: Everyone Is Invited

Contact: Mayumi Thrasher