The capacity region of the multiple access channel with arbitrarilycorrelated sources remains an open problem. Cover, El Gamal and Salehi gave anachievable region in the form of single-letter entropy and mutual informationexpressions, without a single-letter converse. Cover, El Gamal and Salehi alsogave a converse in terms of some n-letter mutual informations, which areincomputable. In this paper, we derive an upper bound for the sum rate of thischannel in a single-letter expression by using spectrum analysis. Theincomputability of the sum rate of Cover, El Gamal and Salehi scheme comes fromthe difficulty of characterizing the possible joint distributions for then-letter channel inputs. Here we introduce a new data processing inequality,which leads to a single-letter necessary condition for these possible jointdistributions. We develop a single-letter upper bound for the sum rate by usingthis single-letter necessary condition on the possible joint distributions.
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