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In the limit of infinite block-lengths, the optimal achievable coding rates in channel coding and lossy data compression are characterized by the channel capacity and the source rate-distortion function, respectively. This paper finds new tight finite-block-length bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the non-asymptotic regime. In this paper, the authors show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the non-asymptotic regime.
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