arXiv2009
This paper considers a random access system where each sender can be in two modes of operation, active or not active, and where the set of active users is available to a common receiver only. Active transmitters encode data into independent streams of information, a subset of which are decoded by the receiver, depending on the value of the collective interference. The main contribution is to present an information-theoretic formulation of the problem which allows us to characterize, with a guaranteed gap to optimality, the rates that can be achieved by different data streams. Our results are articulated as follows. First, we exactly characterize the capacity region of a two-user system assuming a binary-expansion deterministic channel model. Second, we extend this result to a two-user additive white Gaussian noise channel, providing an approximate characterization within $\sqrt{3}/2$ bit of the actual capacity. Third, we focus on the symmetric scenario in which users are active with the same probability and subject to the same received power constraint, and study the maximum achievable expected sum-rate, or throughput, for any number of users. In this case, for the symmetric binary expansion deterministic channel (which is related to the packet collision model used in the networking literature), we show that a simple coding scheme which does not employ superposition coding achieves the system throughput. This result also shows that the performance of slotted ALOHA systems can be improved by allowing encoding rate adaptation at the transmitters. For the symmetric additive white Gaussian noise channel, we propose a scheme that is within one bit of the system throughput for any value of the underlying parameters.