Princeton University

School of Engineering & Applied Science

Information Theory from a Functional Viewpoint

Jingbo Liu
Profs. Cuff and Verdu
Dean's Conference Room, Friend Center
Tuesday, December 12, 2017 - 3:30pm to 5:00pm

A perennial theme of information theory is to find new methods to determine the fundamental limits of various communication systems, which potentially helps the engineers to find better designs by eliminating the deficient ones. Traditional methods (whether it be combinatorial or measure-theoretic) have focused on the notion of ``sets''. This thesis promotes the idea of deriving the fundamental limits using functional inequalities, where the central notion is ``functions'' instead of ``sets''. A functional inequality usually follows from the conventional definition of an information measure by convex duality.
The functional approach not only subsumes the traditional approach (focusing on sets) but also offers strict improvements in certain cases. For example, we resolve the optimal scaling of the second-order rate for the previously open ``side-information problems''. Some ingredients of our work (e.g. single-shot bounds, concentration of measure, functional-analytic tools) have relevance or potential implications for other research areas such as theoretical computer science or high dimensional statistics.