TY - GEN

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

AU - Kontoyiannis, Ioannis

AU - Suhov, Yurii M.

PY - 1994

Y1 - 1994

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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U2 - 10.1109/ISIT.1994.394774

DO - 10.1109/ISIT.1994.394774

M3 - Conference contribution

AN - SCOPUS:34948846002

SN - 0780320158

SN - 9780780320154

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 -