Wasserstein continuity of entropy and outer bounds for interference channels.

Yury Polyanskiy
Assistant Professor, MIT
Given on: April 10th, 2015

Abstract

In this talk I will overview our recent results on behavior of information quantities in Gaussian noise. The unifying theme behind these results is coupling and optimal transportation. In particular, I will show that (under regularity conditions) the differential entropy is a Lipschitz function of the distribution with respect to the Wasserstein distance. The resulting inequality (together with Talagrand's transportation-information inequality) is applied to prove a new outer bound for the Gaussian interference channel, finally settling the "missing corner point" problem of Costa (1985).

Corresponding inequalities and applications are also established for discrete memoryless channels (DMC).

Joint work with Yihong Wu (UIUC).

Bio

Yury Polyanskiy is an Assistant Professor of Electrical Engineering and Computer Science and a member of LIDS at MIT. Yury received the M.S. degree in applied mathematics and physics from the Moscow Institute of Physics and Technology, Moscow, Russia in 2005 and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ in 2010. In 2000-2005 he lead the development of the embedded software in the Department of Surface Oilfield Equipment, Borets Company LLC (Moscow). Currently, his research focuses on basic questions in information theory, error-correcting codes, wireless communication and fault-tolerant and defect-tolerant circuits. Dr. Polyanskiy won the 2013 NSF CAREER award and 2011 IEEE Information Theory Society Paper Award. In 2012 Yury was selected to hold a Robert J. Shillman (1974) Career Development Professorship of EECS.