Generalized channel coding theorems for random multiple access communication

This paper extends the channel coding theorems of [1][2] to time-slotted random multiple access communication systems with a generalized problem formulation. Assume that users choose their channel codes arbitrarily in each time slot. When the codeword length can be taken to infinity, fundamental performance limitation of the system is characterized using an achievable region defined in the space of channel code index vector each specifies the channel codes of all users. The receiver decodes the message if the code index vector happens to locate inside the achievable region and reports a collision if it falls outside the region. A generalized system error performance measure is defined as the maximum of weighted probabilities of different types of communication error events. Upper bounds on the generalized error performance measure are derived under the assumption of a finite codeword length. It is shown that “interfering users” can be introduced to model not only the impact of interference from remote transmitters, but also the impact of channel uncertainty in random access communication.