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The authors consider a discrete memory-less joint source-channel setting. In this setting, if a source sequence is reconstructed with distortion below some threshold, they declare a success event. They prove that for any joint source-channel scheme, if this threshold lowers (better) than the optimum average distortion, then the success probability approaches zero as the block length increases. Furthermore, they show that the probability has an exponential behavior, and evaluate the optimal exponent. Surprisingly, the best exponential behavior is attainable by a separation-based scheme.
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