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We consider the uplink transmission of multimedia services in a cellular network where multiple access is implemented by code division multiple access (CDMA) and the base station performs successive interference cancellation (SIC) to enhance performance. We propose a cross-layer optimization technique that operates both at the physical layer, by selecting the detection order at the SIC receiver, and at the medium access control layer, by selecting the power/rate for each mobile terminal. The optimization objective is the maximization of the overall weighted network throughput with the satisfaction of the quality of service criteria for multimedia communications. The resulting problem turns out to be NP-complete and we resort to a discrete stochastic approximation (DSA) approach for its solution. Concerning DSA, an efficient implementation is proposed in order to reduce memory occupation and improve the convergence of the algorithm. In a UMTS cellular environment, numerical results show that the optimization provides a significant performance advantage over existing techniques at the cost of an increase of computational complexity and memory occupation.