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

Yuval Kochman; Or Ordentlich; Yury Polyanskiy

doi:10.1109/TIT.2020.2983148

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

Yuval Kochman, Or Ordentlich^*, Yury Polyanskiy

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-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 language	American English
Article number	9046817
Pages (from-to)	4722-4741
Number of pages	20
Journal	IEEE Transactions on Information Theory
Volume	66
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2020.2983148
State	Published - Aug 2020

Bibliographical note

Funding Information:
Manuscript received February 21, 2019; revised February 16, 2020; accepted March 7, 2020. Date of publication March 25, 2020; date of current version July 14, 2020. The work of Yuval Kochman was supported in part by the Israel Science Foundation (ISF) under Grant 1555/18; in part by the HUJI Cyber Security Research Center; in part by the Israel National Cyber Bureau in the Prime Minister’s Office; in part by the Ministry of Science and Technology, Israel; in part by the Ministry of Europe and Foreign Affairs; and in part by the Ministry of Higher Education, Research, and Innovation, France. The work of Or Ordentlich was supported by the ISF under Grant 1791/17. The work of Yury Polyanskiy was supported in part by the Center for Science of Information (CSoI) and in part by the NSF Science and Technology Center under Grant CCF-09-39370. This article was presented in part at the 2018 and 2019 IEEE International Symposium on Information Theory. (Corresponding author: Or Ordentlich.) Yuval Kochman and Or Ordentlich are with the Rachel and Selim Benin School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: yuvalko@cs.huji.ac.il; or.ordentlich@mail.huji.ac.il).

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

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

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10.1109/TIT.2020.2983148

Cite this

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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.",

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note = "Funding Information: Manuscript received February 21, 2019; revised February 16, 2020; accepted March 7, 2020. Date of publication March 25, 2020; date of current version July 14, 2020. The work of Yuval Kochman was supported in part by the Israel Science Foundation (ISF) under Grant 1555/18; in part by the HUJI Cyber Security Research Center; in part by the Israel National Cyber Bureau in the Prime Minister{\textquoteright}s Office; in part by the Ministry of Science and Technology, Israel; in part by the Ministry of Europe and Foreign Affairs; and in part by the Ministry of Higher Education, Research, and Innovation, France. The work of Or Ordentlich was supported by the ISF under Grant 1791/17. The work of Yury Polyanskiy was supported in part by the Center for Science of Information (CSoI) and in part by the NSF Science and Technology Center under Grant CCF-09-39370. This article was presented in part at the 2018 and 2019 IEEE International Symposium on Information Theory. (Corresponding author: Or Ordentlich.) Yuval Kochman and Or Ordentlich are with the Rachel and Selim Benin School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: yuvalko@cs.huji.ac.il; or.ordentlich@mail.huji.ac.il). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

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

Abstract

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Keywords

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