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In this paper, we propose contention resolution algorithms for immediate and deferred first-transmission protocols in a multi-packet reception slotted ALOHA system based on code division multiple access. The system employs a central base station that broadcasts the retransmission probability for each slot to all mobile terminals within its coverage. The base station estimates the system backlog by exploiting cross-layer information on multiple access interference. Based on this information, the retransmission probability is chosen in order to maximize the expectation of the system throughput conditioned on the number of retransmitting terminals. The performance of our algorithms and the system stability are evaluated by theoretical analysis and compared to simulations. Under perfect power control it is shown that our algorithms are stable and their performance very closely approaches the analytical upperbound of the system throughput. Under imperfect power control, the simulation result shows that the algorithms remain robust in maintaining 50% throughput efficiency in a coded system with 2 dB in power control errors.