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We consider a multi-user wireless network in which each user has one packet of information to transmit to a central receiver. We study an uncoordinated paradigm where the users send their packet a random number of times according to a probability distribution. Instead of discarding the collided packets, the receiver performs iterative collision resolution. Recently, a few studies have shown that the iterative collision resolution process can be viewed as message-passing decoding on an appropriately defined Tanner graph. Using this equivalence, they used standard techniques to numerically optimize the probability distribution and demonstrated substantial throughput improvement over slotted ALOHA. In this paper, we show that the well-known soliton distribution is an optimal probability distribution and that the resulting throughput efficiency can be arbitrarily close to 1.
Narayanan et al. (Wed,) studied this question.