  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.
