Finite length performance of random MAC strategies

The Internet of Things (IoT) is fueling innovation in nearly every part of our lives. From smart homes, cars, and cities, the Internet of Things is creating a more convenient, secure, intelligent, and personalized experience. While for any final user this IoT vision is a substantial innovation step, for communication providers is a compelling thread with massive number of devices connected to the Internet. Multiple connected devices sharing common wireless resources might create interference if they access the channel simultaneously. Medium access control 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 of 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.