Communicating via a processing broadcast satellite

Three dependent users are physically separated but communicate with each other via a satellite. Each user generates data which it stores locally. In addition, each user sends a message to the satellite. The satellite processes the messages received from the users and broadcasts one common message to all three users. Each user must be capable of reconstructing the data of the other two users based upon the broadcast message and its own stored data. Our problem is to determine the minimum amount of information which must be transmitted to and from the satellite. The solution to this problem is obtained for the case where subsequent data triples that are produced by the users are independent and identically distributed. The three symbols within each triple are assumed to be dependent. Crucial for the solution is an achievability proof that involves cascaded Slepian-Wolf (1973) source coding