A Lower Bound on the Expected Distortion of Joint Source-Channel Coding

Yuval Kochman, Or Ordentlich*, Yury Polyanskiy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of the blocklength n. Our main result is that in general the convergence rate is not faster than n{-1/2}. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least Omega (n{-1/2}) above the asymptotic value, if the 'bandwidth expansion ratio' is above 1.

Original languageAmerican English
Article number9046817
Pages (from-to)4722-4741
Number of pages20
JournalIEEE Transactions on Information Theory
Volume66
Issue number8
DOIs
StatePublished - Aug 2020

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Joint source-channel coding
  • binary symmetric channel (BSC)
  • broadcast channel
  • finite blocklength

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