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This paper addresses the problem of streaming packetized media over a lossy packet network to a wireless client, in a rate-distortion optimized way. We introduce an incremental redundancy error-correction scheme that combats the effects of both packet loss and bit errors in an end-to-end fashion, without support from the underlying network or from an intermediate base station. The scheme is employed within an optimization framework that enables the sender to compute which packets it should send, out of all the packets it could send at a given transmission opportunity, in order to meet an average transmission-rate constraint while minimizing the average end-to-end distortion. Experimental results show that our system is robust and maintains quality of service over a wide range of channel conditions. Up to 8 dB performance gains are registered over systems that are not rate-distortion optimized, at bit-error rates as large as 10-2.