A Single-letter Upper Bound for the Sum Rate of Multiple Access Channels with Correlated Sources

The capacity region of the multiple access channel with arbitrarily 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 gave a converse in terms of some n-letter mutual informations, which are incomputable. In this paper, we derive an upper bound for the sum rate of this channel in a single-letter expression by using spectrum analysis. The incomputability of the sum rate of Cover, El Gamal and Salehi scheme comes from the difficulty of characterizing the possible joint distributions for the n-letter channel inputs. Here we introduce a new data processing inequality, which leads to a single-letter necessary condition for these possible joint distributions. We develop a single-letter upper bound for the sum rate by using this single-letter necessary condition on the possible joint distributions.