Error Exponents and Strong Converse Exponents for Classical Data Compression with Quantum Side Information

Cheng, HC; Hanson, EP; Datta, N; Hsieh, MH

Error Exponents and Strong Converse Exponents for Classical Data Compression with Quantum Side Information

Cheng, HC

Hanson, EP Datta, N Hsieh, MH

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Publication Type:: Conference Proceeding
Citation:: IEEE International Symposium on Information Theory - Proceedings, 2018, 2018-June pp. 2162 - 2166
Issue Date:: 2018-08-15

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Field	Value	Language
dc.contributor.author	Cheng, HC https://orcid.org/0000-0003-4499-4679	en_US
dc.contributor.author	Hanson, EP	en_US
dc.contributor.author	Datta, N	en_US
dc.contributor.author	Hsieh, MH https://orcid.org/0000-0002-3396-8427	en_US
dc.date.issued	2018-08-15	en_US
dc.identifier.citation	IEEE International Symposium on Information Theory - Proceedings, 2018, 2018-June pp. 2162 - 2166	en_US
dc.identifier.isbn	9781538647806	en_US
dc.identifier.issn	2157-8095	en_US
dc.identifier.uri	http://hdl.handle.net/10453/134184
dc.description.abstract	© 2018 IEEE. In this paper, we analyze classical data compression with quantum side information (also known as the classical-quantum Slepian- Wolf protocol) in the so-called large and moderate deviation regimes. In the non-asymptotic setting, the protocol involves compressing classical sequences of finite length n and decoding them with the assistance of quantum side information. In the large deviation regime, the compression rate is fixed, and we obtain bounds on the error exponent function, which characterizes the minimal probability of error as a function of the rate. Devetak and Winter showed that the asymptotic data compression limit for this protocol is given by a conditional entropy. For any protocol with a rate below this quantity, the probability of error converges to one asymptotically and its speed of convergence is given by the strong converse exponent function. We obtain finite blocklength bounds on this function, and determine exactly its asymptotic value, thus improving on previous results by Tomamichel. In the moderate deviation regime for the compression rate, the latter is no longer considered to be fixed. It is allowed to depend on the blocklength n, but assumed to decay slowly to the asymptotic data compression limit. Starting from a rate above this limit, we determine the speed of convergence of the error probability to zero and show that it is given in terms of the conditional information variance. Our results complement earlier results obtained by Tomamichel and Hayashi, in which they analyzed the so-called small deviation regime of this protocol.	en_US
dc.relation.ispartof	IEEE International Symposium on Information Theory - Proceedings	en_US
dc.relation.isbasedon	10.1109/ISIT.2018.8437348	en_US
dc.title	Error Exponents and Strong Converse Exponents for Classical Data Compression with Quantum Side Information	en_US
dc.type	Conference Proceeding
utslib.citation.volume	2018-June	en_US
utslib.for	0806 Information Systems	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	2018-June	en_US

Abstract:

© 2018 IEEE. In this paper, we analyze classical data compression with quantum side information (also known as the classical-quantum Slepian- Wolf protocol) in the so-called large and moderate deviation regimes. In the non-asymptotic setting, the protocol involves compressing classical sequences of finite length n and decoding them with the assistance of quantum side information. In the large deviation regime, the compression rate is fixed, and we obtain bounds on the error exponent function, which characterizes the minimal probability of error as a function of the rate. Devetak and Winter showed that the asymptotic data compression limit for this protocol is given by a conditional entropy. For any protocol with a rate below this quantity, the probability of error converges to one asymptotically and its speed of convergence is given by the strong converse exponent function. We obtain finite blocklength bounds on this function, and determine exactly its asymptotic value, thus improving on previous results by Tomamichel. In the moderate deviation regime for the compression rate, the latter is no longer considered to be fixed. It is allowed to depend on the blocklength n, but assumed to decay slowly to the asymptotic data compression limit. Starting from a rate above this limit, we determine the speed of convergence of the error probability to zero and show that it is given in terms of the conditional information variance. Our results complement earlier results obtained by Tomamichel and Hayashi, in which they analyzed the so-called small deviation regime of this protocol.

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http://hdl.handle.net/10453/134184