A variable-rate lossy joint source-channel coding scheme for burst-noise communication channels with noiseless feedback is introduced. The scheme comprises a multi-stage channel optimized vector quantization system that dynamically allocates bits via a greedy algorithm among the variable-rate residual quantizers at each stage, based on the channel output sequence received at the encoder through the feedback link, thereby generalizing a prior fixed-rate scheme. Simulations over an $M$-th order Markov noise Polya contagion channel demonstrate that the proposed variable-rate scheme consistently outperforms the fixed-rate scheme, regardless of the channel bit error rate and noise correlation, achieving signal-to-noise ratio gains of up to about 4.5 dB.

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