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Prefixes and the entropy rate for long-range sources

Kontoyiannis, I and Suhov, YM (1994) Prefixes and the entropy rate for long-range sources. In: UNSPECIFIED.

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Abstract

The asymptotic a.s.-relation H = limn→∞ n log n ÷ Σi=1n Lin (X) 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 essxinf P(Xn+r | x-∞,n) ≥ α > 0. Here, H is the entropy rate of the process X, and Lin(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.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 18 Aug 2020 12:42
DOI: