Prefixes and the entropy rate for long-range sources

Ioannis Kontoyiannis; Iouri M. Soukhov

doi:10.1109/ISIT.1994.394774

Prefixes and the entropy rate for long-range sources

Ioannis Kontoyiannis, Iouri M. Soukhov

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
Number of pages	1
DOIs	https://doi.org/10.1109/ISIT.1994.394774
State	Published - Dec 1 1994
Event	1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway Duration: Jun 27 1994 → Jul 1 1994

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

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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.",

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

AU - Kontoyiannis, Ioannis

AU - Soukhov, Iouri M.

PY - 1994/12/1

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

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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