An interpretation of the Cover and Leung capacity region for the MAC with feedback through stochastic control

We consider the problem of communication over a multiple access channel (MAC) with noiseless feedback. A single-letter characterization of the capacity of this channel is not currently known in general. We formulate the MAC with feedback capacity problem as a stochastic control problem for a special class of channels for which the capacity is known to be the single-letter expression given by Cover and Leung. This approach has been recently successful in finding channel capacity for point-to-point channels with noiseless feedback but has not yet been fruitful in the study of multi-user communication systems. Our interpretation provides an understanding of the role of auxiliary random variables and can also hint at on-line capacity-achieving transmission schemes.