Slotted ALOHA with compute-and-forward

The benefit of applying compute-and-forward (C&F) to slotted ALOHA (S-ALOHA) systems is studied. A Markov chain model is introduced, and an approximate stability region is given. It is shown that the approximate region is asymptotically exact as the number of users tends to infinity. It is also shown that the approximate region is very accurate even for systems with a small number of users. Further, based on the approximate region, simple expressions for the throughput and delay performance of S-ALOHA with C&F are derived, demonstrating the significant advantages offered by C&F.