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The study of random access protocols has recently regained attention due to new cross-layer schemes such as multipacket reception (MPR) systems and network diversity multiple access protocols (NDMA). Despite their relevance, these two systems have only been simultaneously studied employing finite user population models and considering perfect detection of the active users, which are assumptions only useful in scenarios with low numbers of users and high values of the SNR. The purpose of this paper is to introduce an infinite user population model, valid for scenarios with large numbers of users and finite traffic loads, which allows us to extend the available results on ALOHA MPR protocols to systems that use retransmission diversity (RD). Unlike existing approaches our model includes both the effects of packet decoding errors and the effects of imperfect detection of the active users, which considerably affect the performance of conventional NDMA systems in finite SNR environments. Additionally, the proposed model provides a better approximation to the queuing delay of NDMA protocols than the conventional formula of an M/G/1 queue with vacations. Finally, the proposed algorithm also represents an extension and generalization of contention binary tree algorithms assisted by signal processing tools such as SICTA (successive interference cancellation tree algorithm) and other algorithms assisted by source separation. The benefits of the proposed model are assessed using simulation and analytic results.