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We investigate the problem of optimal channel protection of multiple-description coded (MDC) multimedia contents at a wireless access point (WAP). For each MDC packet, the WAP has the option to protect and broadcast the packet using one of the available channel coders, or to drop the packet altogether. For a fixed FEC-based MDC, we show how this optimization can be approximated by a convex optimization problem with linear constraints, and thus, can be solved efficiently. We verify the validity of our results through extensive simulations of a wireless image streaming application that employs multiple turbo channel coders, where we report gains of more than 2.50 dB PSNR in average reconstruction quality at receivers. We also devise an iterative algorithm for joint optimization of the channel code rate assignment and the design of the MDC. Our simulations show further gains of up to 5.40 dB in average PSNR when this joint optimization is employed.