Keynote Speaker

Abstract

Entropic Vectors, Convex Optimization and Wireless Networks Information theory is well poised to have an impact on the manner in which future networks are designed and maintained, both because wired networks are ripe for applications such as network coding and also because wireless networks cannot be satisfactorily dealt with using conventional networking tools. The challenge is that most network information theory problems are notoriously difficult and so the barriers that must be overcome are often quite high. In particular, there are only a limited number of tools available and so fresh approaches are quite welcome. We describe an approach based on the definition of the space of "normalized" entropic vectors. In this framework, for a large class of acyclic memoryless networks, the capacity region for an arbitrary set of sources and destinations can be found by maximization of a linear function over the set of channel-constrained normalized entropic vectors and some linear constraints. The key point is that the closure of this set is convex and compact. While this may not necessarily make the problem simpler, it certainly circumvents the "infinite-letter characterization" issue, as well as the nonconvexity of earlier formulations. It also exposes the core of the problem as that of determining the space of normalized entropic vectors.