Lossy Joint Source-Channel Coding in the Finite Blocklength Regime

Abstract

This paper finds new tight finite-blocklength 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 nonasymptotic regime. A joint source-channel code maps a block of k source symbols onto a length- n channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability ε that the distortion exceeds a given threshold d . For memoryless sources and channels, it is demonstrated that the parameters of the best joint source-channel code must satisfy nC - kR( d ) ≈ √( nV + k V ( d )) Q^(-1) (ε), where C and V are the channel capacity and channel dispersion, respectively; R ( d ) and V ( d ) are the source rate-distortion and rate-dispersion functions; and Q is the standard Gaussian complementary cumulative distribution function. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and channel satisfy a certain probabilistic matching condition. In this paper, we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the nonasymptotic regime.

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