Third-order coding rate for universal compression of Markov sources

Nematollah Iri; Oliver Kosut

doi:10.1109/ISIT.2015.7282805

Third-order coding rate for universal compression of Markov sources

Nematollah Iri, Oliver Kosut

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

14 Scopus citations

Abstract

We consider the universal source coding problem for first-order stationary, irreducible and aperiodic Markov sources for short blocklengths. Achievability is derived based on the previously introduced algorithm for universal compression of memoryless sources in the finite blocklengths, the Type Size Code, which encodes strings based on type class size. We derive the third-order asymptotic coding rate of the Type Size code for this model class. We also present a converse on the third-order coding rate for the general class of fixed-to-variable codes and show the optimality of Type Size codes for such Markov sources.

Original language	English (US)
Title of host publication	Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1996-2000
Number of pages	5
ISBN (Electronic)	9781467377041
DOIs	https://doi.org/10.1109/ISIT.2015.7282805
State	Published - Sep 28 2015
Event	IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: Jun 14 2015 → Jun 19 2015

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2015-June
ISSN (Print)	2157-8095

Other

Other	IEEE International Symposium on Information Theory, ISIT 2015
Country/Territory	Hong Kong
City	Hong Kong
Period	6/14/15 → 6/19/15

Keywords

Data compression
Markov sources
finite blocklengh analysis
third-order coding rate
universal source coding

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2015.7282805

Cite this

Iri, N., & Kosut, O. (2015). Third-order coding rate for universal compression of Markov sources. In Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 (pp. 1996-2000). Article 7282805 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2015.7282805

Third-order coding rate for universal compression of Markov sources. / Iri, Nematollah; Kosut, Oliver.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1996-2000 7282805 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2015-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Iri, N & Kosut, O 2015, Third-order coding rate for universal compression of Markov sources. in Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015., 7282805, IEEE International Symposium on Information Theory - Proceedings, vol. 2015-June, Institute of Electrical and Electronics Engineers Inc., pp. 1996-2000, IEEE International Symposium on Information Theory, ISIT 2015, Hong Kong, Hong Kong, 6/14/15. https://doi.org/10.1109/ISIT.2015.7282805

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title = "Third-order coding rate for universal compression of Markov sources",

abstract = "We consider the universal source coding problem for first-order stationary, irreducible and aperiodic Markov sources for short blocklengths. Achievability is derived based on the previously introduced algorithm for universal compression of memoryless sources in the finite blocklengths, the Type Size Code, which encodes strings based on type class size. We derive the third-order asymptotic coding rate of the Type Size code for this model class. We also present a converse on the third-order coding rate for the general class of fixed-to-variable codes and show the optimality of Type Size codes for such Markov sources.",

keywords = "Data compression, Markov sources, finite blocklengh analysis, third-order coding rate, universal source coding",

author = "Nematollah Iri and Oliver Kosut",

note = "Funding Information: This work was supported in part by the National Science Foundation under grant CCF-1422358. Publisher Copyright: {\textcopyright} 2015 IEEE.; IEEE International Symposium on Information Theory, ISIT 2015 ; Conference date: 14-06-2015 Through 19-06-2015",

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AB - We consider the universal source coding problem for first-order stationary, irreducible and aperiodic Markov sources for short blocklengths. Achievability is derived based on the previously introduced algorithm for universal compression of memoryless sources in the finite blocklengths, the Type Size Code, which encodes strings based on type class size. We derive the third-order asymptotic coding rate of the Type Size code for this model class. We also present a converse on the third-order coding rate for the general class of fixed-to-variable codes and show the optimality of Type Size codes for such Markov sources.

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BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015

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ER -

Third-order coding rate for universal compression of Markov sources

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Keywords

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