Relationship among Complexities of Individual Sequences over Countable Alphabet

Shigeaki KUZUOKA; Tomohiko UYEMATSU

doi:10.1093/ietfec/e89-a.7.2047

Relationship among Complexities of Individual Sequences over Countable Alphabet

Shigeaki KUZUOKA, Tomohiko UYEMATSU

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This paper investigates some relations among four complexities of sequence over countably infinite alphabet, and shows that two kinds of empirical entropies and the self-entropy rate regarding a Markov source are asymptotically equal and lower bounded by the maximum number of phrases in distinct parsing of the sequence. Some connections with source coding theorems are also investigated.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.7 pp.2047-2055

Publication Date: 2006/07/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.7.2047

Type of Manuscript: PAPER

Category: Information Theory

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Shigeaki KUZUOKA, Tomohiko UYEMATSU, "Relationship among Complexities of Individual Sequences over Countable Alphabet" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 7, pp. 2047-2055, July 2006, doi: 10.1093/ietfec/e89-a.7.2047.
Abstract: This paper investigates some relations among four complexities of sequence over countably infinite alphabet, and shows that two kinds of empirical entropies and the self-entropy rate regarding a Markov source are asymptotically equal and lower bounded by the maximum number of phrases in distinct parsing of the sequence. Some connections with source coding theorems are also investigated.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.7.2047/_p

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@ARTICLE{e89-a_7_2047,
author={Shigeaki KUZUOKA, Tomohiko UYEMATSU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Relationship among Complexities of Individual Sequences over Countable Alphabet},
year={2006},
volume={E89-A},
number={7},
pages={2047-2055},
abstract={This paper investigates some relations among four complexities of sequence over countably infinite alphabet, and shows that two kinds of empirical entropies and the self-entropy rate regarding a Markov source are asymptotically equal and lower bounded by the maximum number of phrases in distinct parsing of the sequence. Some connections with source coding theorems are also investigated.},
keywords={},
doi={10.1093/ietfec/e89-a.7.2047},
ISSN={1745-1337},
month={July},}

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TY - JOUR
TI - Relationship among Complexities of Individual Sequences over Countable Alphabet
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2047
EP - 2055
AU - Shigeaki KUZUOKA
AU - Tomohiko UYEMATSU
PY - 2006
DO - 10.1093/ietfec/e89-a.7.2047
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2006
AB - This paper investigates some relations among four complexities of sequence over countably infinite alphabet, and shows that two kinds of empirical entropies and the self-entropy rate regarding a Markov source are asymptotically equal and lower bounded by the maximum number of phrases in distinct parsing of the sequence. Some connections with source coding theorems are also investigated.
ER -