Irregular Repetition Slotted ALOHA over the Rayleigh Block Fading Channel with Capture

Random access protocols relying on the transmission of packet replicas in multiple slots and exploiting interference cancellation at the receiver have been shown to achieve per- formance competitive with that of orthogonal schemes. So far the optimization of the repetition degree profile, defining the probability for a user to transmit a given number of replicas, has mainly been performed targeting the collision channel model. In this paper the analysis is extended to a block fading channel model, also assuming capture effect at the receiver. Density evolution equations are developed for the new setting and, based on them, some repetition degree profiles are optimized and analyzed via Monte Carlo simulation in a finite frame length setting. The derived distributions are shown to achieve throughputs largely exceeding 1 [packet/slot].