On the asymptotic optimality of coded slotted Aloha random access systems

We consider a slotted Aloha random access system with combined coding and power/retransmission control. Under suitable conditions, if M or fewer users transmit simultaneously, they are successfully decoded with high probability, with M depending on coding rate and SINR. We show then that, among any realizable random access protocol, slotted Aloha's spectral efficiency and maximum throughput are asymptotically optimal as the coding rate vanishes.