Finite length analysis of irregular repetition slotted Aloha (IRSA) access protocols

In this paper the error rate of irregular repetition slotted ALOHA (IRSA) access protocols, under successive interference cancellation decoding, is analyzed for a finite number of active users and in a finite frame length setting. The considered channel model is a collision channel where collisions are destructive and where packets not experiencing collisions are always correctly received. An expression for the expected number of stopping sets for given variable and check nodes actual distributions is first derived and this expression is then used to upper bound the error probability of any IRSA scheme. Monte Carlo simulations exhibit a very good match with the proposed analytical tool.