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In this paper, we present a novel analytical framework for the study of a multiple access scheme for an ad hoc code division multiple access (CDMA) network with hybrid automatic repeat request (HARQ) error control and matched filter linear successive interference cancellation receivers. Unlike most prior work on Multi-User Detection (MUD), we directly address networking issues. In particular, we develop an approach based on renewal and semi-Markov processes, that accurately accounts for the statistical dependencies between interference, coding rate, and performance in a multiple access system. We show that our approximate approach can accurately predict throughput and failure rate values, and present results for a specific system, providing useful insight on issues related to the use of HARQ error control and MUD receivers in CDMA ad hoc networks.