Lossy joint source-channel coding in the finite blocklength regime

This paper shows 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 non-asymptotic 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 + kV(d)) Q^-1 (ϵ), where C and V are the channel capacity and dispersion, respectively; R(d) and V(d) are the source rate-distortion and rate-dispersion functions; and Q is the standard Gaussian complementary cdf.