The Region of Achievable Rates for Multiterminal Source Coding–Part I

It is proved that a convexified form of the Berger-Tung inner bound provides the set of all achievable rates for the multiterminal source coding problem. In this paper, a proof is developed for general discrete memoryless sources and bounded distortion measures, for two encoding terminals. The proof is based on two new developments. One is the construction of new inner and outer bounds to the rate region, with the property that both are defined over the same class of probability distributions, thus making them directly comparable. Another is a series of lemmas about properties of covers induced by generic distributed codes, which show that Berger-Tung codes induce covers of maximum size. This result constitutes a solution to an open problem in network information theory, whose formulation dates back to at least 1973.