On the Capacity of Slotted Aloha With Ancillary Channels

In this letter, we focus on a legacy system operated with slotted-Aloha and complemented by a redundancy channel where nodes transmit replicas of their packets. The number of replicas follows a probability distribution, and successive interference cancelation is applied across channels. Leaning on the theory of codes on graphs and algebraic tools, we prove that the system can provide arbitrarily small error rate up to a certain load, beyond which packet losses have to be undergone with finite probability. Tight upper bounds on capacity are derived for both regions, characterizing the achievable performance as a function of the deployed ancillary resources. Simulation results for moderate MAC frame length are also provided.