The recent research has established an analogy between successive
interference cancellation in slotted ALOHA framework and iterative
belief-propagation erasure-decoding, which has opened the possibility to
enhance random access protocols by utilizing theory and tools of
erasure-correcting codes. In this paper we present a generalization of the
and-or tree evaluation, adapted for the asymptotic analysis of the slotted
ALOHA-based random-access protocols, for the case when the contending users
experience different channel conditions, resulting in packet loss probability
that varies across users. We apply the analysis to the example of frameless
ALOHA, where users contend on a slot basis. We present results regarding the
optimal access probabilities and contention period lengths, such that the
throughput and probability of user resolution are maximized.Comment: 4 pages, submitted to GlobalSIP 201
