Finite-Length Analysis of Irregular Repetition Slotted ALOHA in the Waterfall Region

A finite-length analysis is introduced for irregular repetition slotted ALOHA (IRSA) that enables to accurately estimate its performance in the moderate-to-high packet loss probability regime, i.e., in the so-called waterfall region. The analysis is tailored to the collision channel model, which enables mapping the description of the successive interference cancellation process onto the iterative erasure decoding of low-density parity-check codes. The analysis provides accurate estimates of the packet loss probability of IRSA in the waterfall region as demonstrated by Monte Carlo simulations.