The capacities of fundamental communication problems such as channels with feedback and two-way communications channels are characterized with multi-letter expressions. The challenge in simplifying these expressions is their exhaustive dependence on all information that is accumulated throughout the communication. In this talk, we aim to simplify such capacities by imposing a structure on the accumulated data via a new sequential quantization technique on a directed graph.
First application of this method is for channels with memory and feedback. We will show upper and lower single-letter bounds on the capacity. The bounds are expressed with structured auxiliary random variable (r.v.), a notion that suits problems of sequential nature. For all cases where the capacity is known, the bounds are tight (with small cardinality of the structured auxiliary r.v.). This reveals a simple capacity formula that captures the major role of structure in feedback problems. We will also present a simple and sequential coding scheme, which is based on the posterior matching principle, and achieves the lower bound (and the capacity in many cases).
As time permits, we will show that structure is beneficial for other communication scenarios such as two-way communication channels with common outputs and the energy harvesting model.
The talk is based on a joint work with Prof. Henry Pfister (Duke Univeristy), Prof. Haim Permuter (BGU) and Prof. Navin Kashyap (IISc).
Oron Sabag received his B.Sc. and M.Sc. (both with honors) in Electrical and Computer Engineering from Ben-Gurion University, Israel, in 2013 and 2016, respectively. He is currently pursuing his Ph.D. in the direct track program, under the supervision of Prof. Haim Permuter. Oron is a recipient of several awards, among them are the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award, the SPCOM-2016 Best Student Paper Award, the Lachish Fellowship, and the Feder Family Award for outstanding research in the field of communications.