A stochastic control interpretation of the Cover and Leung region for the MAC with noiseless feedback

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. Several schemes exist in the literature that provide achievable region expressions involving a number of auxiliary variables. A series of recent results in point-to-point communications with noiseless feedback study the information theoretic problem of finding channel capacity in a stochastic control framework. This approach has not yet been fruitful in the study of multi-user communication scenaria. In this paper 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 Cover and Leung region. This interpretation provides an understanding of the role of auxiliary random variables. In addition, through this interpretation a useful single-letter outer bound is derived. For the special case studied in this paper, this outer bound is tight.