Finite Length Performance of Random Slotted ALOHA Strategies

Multiple connected devices sharing common wireless resources might create interference if they access the channel simultaneously. Medium access control (MAC) protocols generally regulate the access of the devices to the shared channel to limit signal interference. In particular, irregular repetition slotted ALOHA (IRSA) techniques can achieve high-throughput performance when interference cancellation methods are adopted to recover from collisions. In this work, we study the finite length performance for IRSA schemes by building on the analogy between successive interference cancellation and iterative belief-propagation on erasure channels. We use a novel combinatorial derivation based on the matrix-occupancy theory to compute the error probability and we validate our method with simulation results.