Multiterminal rate/distortion theory deals with data compression problems in which multiple dependent sources are encoded separately, subject to fidelity criteria. In this talk, we focus on the problem with two encoding terminals, general discrete memoryless sources and per-letter distortion measures. For this setup, inner and outer bounds to the rate region were developed by Berger and Tung in 1978; these bounds, in general, do not coincide. I will present the construction of a new rate region, that contains the region of the Berger-Tung inner bound, that is contained in the region of the Berger-Tung outer bound, and for which we have established both an achievability result and a matching converse. The proof is based on two new developments. One is the construction of new (and seemingly uncomputable) inner and outer bounds, with the property that both are defined over the same class of probability distributions, thus making them directly comparable. Another is the identification of a structural constraint on the covers of the product source resulting from the requirement of separate encoding, from which an interesting optimality property follows for Berger-Tung codes.
This result constitutes a solution to an open problem in network
information theory, whose formulation dates back to at least 1973.
Link to talk slides