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Multimedia data often have different levels of importance such that more important bits are less error-tolerant. A new rate control method for transporting such multimedia data over parallel wireless links with heterogeneous reliability is proposed. Rate-controlled parallel transmissions (RCPT) of different layers of a multimedia stream with different levels of importance over a wireless channel that support multiple links with heterogeneous reliability can improve the efficiency in resource allocation while satisfying the quality of service requirement of the multimedia connection. To exploit RCPT, we present and evaluate a novel dynamic resource allocation method that decomposes the available radio resources into multiple sets of links with different levels of reliability. We mathematically formulate a rate control problem for the flexible RCPT scheme and develop an efficient real-time resource allocation algorithm with a remarkably fast rate of convergence. Simulation results show that the proposed method improves the utility and reduces the power consumed for delivery of a multimedia stream at the required quality of service, in comparison with a previous scheme, where different layers of each multimedia class are scheduled with dependency, and two schemes that provide homogeneous high or low reliability over all parallel links.