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 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(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 cdf. 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 non-asymptotic regime