A Control Theoretic Interpretation for the Capacity Region of the MAC with Feedback

We consider the problem of communication over a discrete memoryless multiple access channel (DM-MAC) with noiseless feedback. A single-letter characterization of the capacity of this channel is not currently known. Several inner and outer bounds exist in the literature that provide expressions involving a number of auxiliary variables. In this paper we formulate the MAC with feedback capacity problem as a distributed stochastic control problem. Through this interpretation a single-letter outer bound is derived. Although this bound is larger than existing outer bounds in general, for the special class of channels for which the capacity is known to be the Cover and Leung region, the bound is tight. Furthermore, the new formulation provides an interpretation of the auxiliary random variables that usually appear in relevant inner and outer bounds.