Prefixes and the entropy rate for long-range sources

Ioannis Kontoyiannis; Yurii M. Suhov

doi:10.1109/ISIT.1994.394774

Prefixes and the entropy rate for long-range sources

Ioannis Kontoyiannis, Yurii M. Suhov

Mathematics

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

4 Scopus citations

Abstract

The asymptotic a.s.-relation [eqution presented] is derived for any finite-valued stationary ergodic process X=(X_n, n ∈Z) that satisfies a Doeblin-type condition: there exists r ≥ 1 such that [eqution presented]. Here, H is the entropy rate of the process X, and L_i ⁿ(X) is the length of a shortest prefix in X which is initiated at time i and is not repeated among the prefixes initiated at times j, 1 ≤ i ≠ J ≤ n. The validity of this limiting result was established by Shields in 1989 for i.i.d. processes and also for irreducible aperiodic Markov chains. Under our new condition, we prove that this holds for a wider class of processes, that may have infinite memory.

Original language	English (US)
Title of host publication	Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	194
Number of pages	1
ISBN (Print)	0780320158, 9780780320154
DOIs	https://doi.org/10.1109/ISIT.1994.394774
State	Published - 1994
Event	1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway Duration: Jun 27 1994 → Jul 1 1994

Publication series

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

Other

Other	1994 IEEE International Symposium on Information Theory, ISIT 1994
Country/Territory	Norway
City	Trondheim
Period	6/27/94 → 7/1/94

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.1994.394774

Cite this

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title = "Prefixes and the entropy rate for long-range sources",

abstract = "The asymptotic a.s.-relation [eqution presented] is derived for any finite-valued stationary ergodic process X=(Xn, n ∈Z) that satisfies a Doeblin-type condition: there exists r ≥ 1 such that [eqution presented]. Here, H is the entropy rate of the process X, and Li n(X) is the length of a shortest prefix in X which is initiated at time i and is not repeated among the prefixes initiated at times j, 1 ≤ i ≠ J ≤ n. The validity of this limiting result was established by Shields in 1989 for i.i.d. processes and also for irreducible aperiodic Markov chains. Under our new condition, we prove that this holds for a wider class of processes, that may have infinite memory.",

author = "Ioannis Kontoyiannis and Suhov, {Yurii M.}",

year = "1994",

doi = "10.1109/ISIT.1994.394774",

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series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "194",

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note = "1994 IEEE International Symposium on Information Theory, ISIT 1994 ; Conference date: 27-06-1994 Through 01-07-1994",

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Kontoyiannis, I & Suhov, YM 1994, Prefixes and the entropy rate for long-range sources. in Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994., 394774, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 194, 1994 IEEE International Symposium on Information Theory, ISIT 1994, Trondheim, Norway, 6/27/94. https://doi.org/10.1109/ISIT.1994.394774

Prefixes and the entropy rate for long-range sources. / Kontoyiannis, Ioannis; Suhov, Yurii M.
Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994. Institute of Electrical and Electronics Engineers Inc., 1994. p. 194 394774 (IEEE International Symposium on Information Theory - Proceedings).

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

TY - GEN

T1 - Prefixes and the entropy rate for long-range sources

AU - Kontoyiannis, Ioannis

AU - Suhov, Yurii M.

PY - 1994

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N2 - The asymptotic a.s.-relation [eqution presented] is derived for any finite-valued stationary ergodic process X=(Xn, n ∈Z) that satisfies a Doeblin-type condition: there exists r ≥ 1 such that [eqution presented]. Here, H is the entropy rate of the process X, and Li n(X) is the length of a shortest prefix in X which is initiated at time i and is not repeated among the prefixes initiated at times j, 1 ≤ i ≠ J ≤ n. The validity of this limiting result was established by Shields in 1989 for i.i.d. processes and also for irreducible aperiodic Markov chains. Under our new condition, we prove that this holds for a wider class of processes, that may have infinite memory.

AB - The asymptotic a.s.-relation [eqution presented] is derived for any finite-valued stationary ergodic process X=(Xn, n ∈Z) that satisfies a Doeblin-type condition: there exists r ≥ 1 such that [eqution presented]. Here, H is the entropy rate of the process X, and Li n(X) is the length of a shortest prefix in X which is initiated at time i and is not repeated among the prefixes initiated at times j, 1 ≤ i ≠ J ≤ n. The validity of this limiting result was established by Shields in 1989 for i.i.d. processes and also for irreducible aperiodic Markov chains. Under our new condition, we prove that this holds for a wider class of processes, that may have infinite memory.

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M3 - Conference contribution

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T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 194

BT - Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 1994 IEEE International Symposium on Information Theory, ISIT 1994

Y2 - 27 June 1994 through 1 July 1994

ER -

Prefixes and the entropy rate for long-range sources

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