A new upper bound for a binary additive noisy multiple access channel with feedback

We use the idea of dependence balance [1] to obtain the first improvement over the cut-set bound for the discrete memoryless multiple access channel with noiseless feedback (MAC-FB). More specifically, we consider a binary additive noisy MAC-FB whose capacity does not coincide with the Cover-Leung achievable rate region [2]. Evaluating the dependence balance bound is difficult due to an involved auxiliary random variable. We overcome this difficulty by using functional analysis to explicitly evaluate our upper bound for the binary additive noisy MAC-FB and show that it is strictly less than the cut-set bound for the symmetric-rate point on the capacity region.