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We propose a multiresolution algorithm to jointly optimize a source coder and channel coder. The variable-rate source coder combines an optimal bit-allocation strategy and efficient stack-run coding. This compression scheme, concatenated with appropriate rate-compatible punctured convolutional codes, provides a competitive approach to state-of-the-art extensions of zerotree methods to noisy channels. Results show that under the assumption of almost zero probability of decoding error, the proposed scheme provides good performance for a lower complexity.