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The authors 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. They 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.
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