A Coding Theorm for Multiple Access Channels With Correlated Sources

The mathematical theory of communication has been concerned, for the most part, with the reliable transmission of information from a single information source to a single user. An extensive literature exists f J. K. Wolf is Professor of Electrical Engineering at the University of Massachusetts, Amherst, Mass. Partial support for his research on this paper was furnished by the Air Force Office of Scientific Research under contract F-44620-72-C-0085. 1037 1038 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1 9 7 3 on this problem: the basic concepts are contained in the classic papers of Shannon. 1 In this work we consider the case in which messages from a set of information sources are communicated over a common channel to a single receiver. We impose constraints on the encoding techniques which can be employed. A precise formulation of the problem is presented in a subsequent section. Here we describe in less mathematical terms the type of problem considered. A particular multiple access communication channel with two inputs and one output is shown in Fig. 1. Here the two inputs, XI and X2) and the output Y each take values from the set {0, 1). The conditional probability of the output Y for each of the four possible input pairs {X, X2) is also shown in the schema at the right in Fig. 1. It is clear that if the transmitters can cooperate with each other they can transmit without error one bit per channel use by transmitting either the pair (Xi = 0, X2 = 0) or the pair ( X I = 1, X2 = 1).