An Outer Bound for Multiple Access Channels with Correlated Sources

The capacity region of the multiple access channel with correlated sources remains an open problem. Cover, El Gamal and Salehi gave an achievable region in the form of single-letter entropy and mutual information expressions, without a single-letter converse. Cover, El Gamal and Salehi also suggested a converse in terms of some n-letter mutual informations, which are incomputable. We have proposed an upper bound for the sum rate of this channel in a single-letter expression, by utilizing a new necessary condition for the Markov chain constraint on the valid channel input distributions. In this paper, we extend our results from the sum rate to the entire capacity region. We obtain an outer bound for the capacity region of the multiple access channel with correlated sources in finite-letter expressions.