A Coding Theorem for Multiple Access Channels With Correlated Sources

A communication system is studied in which two users communicate with one receiver over a common discrete memoryless channel. The information to be transmitted by the users may be correlated. Their information rates are described by a point in a suitably defined three-dimensional rate space. A point in this rate space is called admissible if there exist coders and decoders for the channel that permit the users to transmit information over it at the corresponding rates with arbitrarily small error probability. The closure of the set of all admissible rate points is called the capacity region, and is the natural generalization of channel capacity to this situation. In this paper we show that e, which depends only on the channel, is convex and we give formulas to determine it exactly. Several simple channels are treated in detail and their capacity regions given explicitly.