Lossy joint source-channel coding in the finite blocklength regime

TL;DR

This paper derives tight finite-blocklength bounds for lossy joint source-channel coding, demonstrating the performance advantages over separate coding and analyzing the effectiveness of symbol-by-symbol transmission in non-asymptotic regimes.

Contribution

It provides new finite-blocklength bounds for joint source-channel coding and compares their performance to separate coding and symbol-by-symbol transmission strategies.

Findings

Joint source-channel coding outperforms separate coding in the finite blocklength regime.

Finite-blocklength bounds relate code parameters to channel and source characteristics.

Symbol-by-symbol transmission can be optimal even without probabilistic matching.

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 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 $\epsilon$ 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 $nC - kR(d) \approx \sqrt{nV + k \mathcal V(d)} Q(\epsilon)$, where $C$ and $V$ are the channel capacity and channel dispersion, respectively; $R(d)$ and $\mathcal V(d)$ 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.