Unrecovered Users Distribution in Coded Random Access Systems with Erasures

In this paper, we consider the problem of estimating the number of unrecovered active users in a coded random access systems over a collision channel with both packet erasures and slot erasures. Each user transmits multiple packet replicas in random slots of the frame and successive interference cancellation (SIC) is exploited at the receiver. Each packet replica is transmitted over an erasure channel. Moreover, the whole signal received in a slot may be erased, making the slot content useless. The developed algorithm can track over SIC iterations the probability distribution of the sought number of users, given all information that it is possible to gather through SIC iterations. The algorithm is validated by numerical simulation, showing that it can considerably reduce the mean square error of the estimation process.