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Access reservation based on slotted ALOHA is commonly used in wirelesscellular access. In this paper we investigate its enhancement based on the useof physical-layer network coding and signature coding, whose main feature isenabling simultaneous resolution of up to K users contending for access, whereK >= 1. We optimise the slot access probability such that the expectedthroughput is maximised. In particular, the slot access probability is chosenin line with an estimate of the number of users in the system that is obtainedrelying on the pseudo-Bayesian approach by Rivest, which we generalise for thecase that K > 1. Under the assumption that this estimate reflects the actualnumber of users, we show that our approach achieves throughput 1 in the limitof large K.

A Pseudo-Bayesian Approach to Sign-Compute-Resolve Slotted ALOHA