Lossy Joint Source-Channel Coding in the Finite Blocklength Regime

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.