  We use the idea of dependence balance to obtain a new outer bound for the
capacity region of the discrete memoryless multiple access channel with
noiseless feedback (MAC-FB). We consider a binary additive noisy MAC-FB whose
feedback capacity is not known. The binary additive noisy MAC considered in
this paper can be viewed as the discrete counterpart of the Gaussian MAC-FB.
Ozarow established that the capacity region of the two-user Gaussian MAC-FB is
given by the cut-set bound. Our result shows that for the discrete version of
the channel considered by Ozarow, this is not the case. Direct evaluation of
our outer bound is intractable due to an involved auxiliary random variable
whose large cardinality prohibits an exhaustive search. We overcome this
difficulty by using functional analysis to explicitly evaluate our outer bound.
Our outer bound is strictly less than the cut-set bound at all points on the
capacity region where feedback increases capacity. In addition, we explicitly
evaluate the Cover-Leung achievable rate region for the binary additive noisy
MAC-FB in consideration. Furthermore, using the tools developed for the
evaluation of our outer bound, we also explicitly characterize the boundary of
the feedback capacity region of the binary erasure MAC, for which the
Cover-Leung achievable rate region is known to be tight. This last result
confirms that the feedback strategies developed by Kramer for the binary
erasure MAC are capacity achieving.
