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 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.
Original language | English (US) |
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Article number | 6408177 |
Pages (from-to) | 2545-2575 |
Number of pages | 31 |
Journal | IEEE Transactions on Information Theory |
Volume | 59 |
Issue number | 5 |
DOIs | |
State | Published - 2013 |
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences
Keywords
- Achievability
- Shannon theory
- converse
- finite blocklength regime
- joint source-channel coding (JSCC)
- lossy source coding
- memoryless sources
- rate-distortion theory