Stochastic Systems Group  

Euclidean Approximation to Information Geometry and Its Applications
Lizhong Zheng
LIDS, MIT
Classical information theory results often take the form of optimizations of entropy and mutual information, which can be viewed as KL divergences, measuring in some sense the "distance" between probability distributions. In more complex problems, such as multiterminal problems, dynamic channels, or when error exponent is of interests, many high dimensional distributions are often involved. Describing the problems and their solutions often requires describing the relation among these high dimensional objects, and the divergence as a distance measure appears to be ineffective for the job. In this talk, we give some examples to demonstrate that a geometric structure for the space of probability distributions can be very powerful in visualizing the solutions to some multiuser communication problems. We will mainly focus on a specific approximation of the local geometry, and apply that to two problems: 1) Gallager's classical results on broadcasting channel; 2) some new results on Gaussian interference channel.
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