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Fumio KANAYA, Jun MURAMATSU, "An Almost Sure Recurrence Theorem with Distortion for Stationary Ergodic Sources" in IEICE TRANSACTIONS on Fundamentals,
vol. E80-A, no. 11, pp. 2264-2267, November 1997, doi: .
Abstract: Let {Xk}k=- be a stationary and ergodic information source, where each Xk takes values in a standard alphabet A with a distance function d: A A [0, ) defined on it. For each sample sequence X = (, x-1, x0, x1, ) and D > 0 let the approximate D-match recurrence time be defined by Rn (x, D) = min {m n: dn (Xn1, Xm+nm+1) D}, where Xji denotes the string xixi+1 xj and dn: An An [0, ) is a metric of An induced by d for each n. Let R (D) be the rate distortion function of the source {Xk}k=- relative to the fidelity criterion {dn}. Then it is shown that lim supn-1/n log Rn (X, D) R (D/2) a. s.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_11_2264/_p
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@ARTICLE{e80-a_11_2264,
author={Fumio KANAYA, Jun MURAMATSU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Almost Sure Recurrence Theorem with Distortion for Stationary Ergodic Sources},
year={1997},
volume={E80-A},
number={11},
pages={2264-2267},
abstract={Let {Xk}k=- be a stationary and ergodic information source, where each Xk takes values in a standard alphabet A with a distance function d: A A [0, ) defined on it. For each sample sequence X = (, x-1, x0, x1, ) and D > 0 let the approximate D-match recurrence time be defined by Rn (x, D) = min {m n: dn (Xn1, Xm+nm+1) D}, where Xji denotes the string xixi+1 xj and dn: An An [0, ) is a metric of An induced by d for each n. Let R (D) be the rate distortion function of the source {Xk}k=- relative to the fidelity criterion {dn}. Then it is shown that lim supn-1/n log Rn (X, D) R (D/2) a. s.},
keywords={},
doi={},
ISSN={},
month={November},}
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TY - JOUR
TI - An Almost Sure Recurrence Theorem with Distortion for Stationary Ergodic Sources
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2264
EP - 2267
AU - Fumio KANAYA
AU - Jun MURAMATSU
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1997
AB - Let {Xk}k=- be a stationary and ergodic information source, where each Xk takes values in a standard alphabet A with a distance function d: A A [0, ) defined on it. For each sample sequence X = (, x-1, x0, x1, ) and D > 0 let the approximate D-match recurrence time be defined by Rn (x, D) = min {m n: dn (Xn1, Xm+nm+1) D}, where Xji denotes the string xixi+1 xj and dn: An An [0, ) is a metric of An induced by d for each n. Let R (D) be the rate distortion function of the source {Xk}k=- relative to the fidelity criterion {dn}. Then it is shown that lim supn-1/n log Rn (X, D) R (D/2) a. s.
ER -