A pseudo-Bayesian approach to sign-compute-resolve slotted ALOHA

Access reservation based on slotted ALOHA is commonly used in wireless cellular access. In this paper we investigate its enhancement based on the use of physical-layer network coding and signature coding, whose main feature is enabling simultaneous resolution of up to K users contending for access, where K >= 1. We optimise the slot access probability such that the expected throughput is maximised. In particular, the slot access probability is chosen in line with an estimate of the number of users in the system that is obtained relying on the pseudo-Bayesian approach by Rivest, which we generalise for the case that K > 1. Under the assumption that this estimate reflects the actual number of users, we show that our approach achieves throughput 1 in the limit of large K