Capacity and Coding for T Active Users Out of M on the Collision Channel

The problem of designing codes for M users that permit any T < M users to transmit at the same time is investigated for the collision channel. Twelve communication problems are considered that vary according to the degree of synchronization among users, the receiver's knowledge of the active users, and the desired reliability of the code. For each problem, the T-of-M user capacity region is determined and constructive coding schemes that approach any rate in this region are presented. Applications to random access communications are discussed.