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This paper proposes three new information measures for individual sequences and clarifies their properties. Our new information measures are called as the non-overlapping max-entropy, the overlapping smooth max-entropy, and the non-overlapping smooth max-entropy, respectively. These measures are related to the fixed-length coding of individual sequences. We investigate these measures, and show the following three properties: (1) The non-overlapping max-entropy coincides with the topological entropy. (2) The overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the Ziv-entropy. (3) When an individual sequence is drawn from an ergodic source, the overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the entropy rate of the source. Further, we apply these information measures to the fixed-length coding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E107-A No.3 pp.393-403

- Publication Date
- 2024/03/01

- Publicized
- 2023/08/16

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2023TAP0005

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Source Coding and Data Compression

Tomohiko UYEMATSU

Tokyo Institute of Technology

Tetsunao MATSUTA

Saitama University

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Tomohiko UYEMATSU, Tetsunao MATSUTA, "Equivalences among Some Information Measures for Individual Sequences and Their Applications for Fixed-Length Coding Problems" in IEICE TRANSACTIONS on Fundamentals,
vol. E107-A, no. 3, pp. 393-403, March 2024, doi: 10.1587/transfun.2023TAP0005.

Abstract: This paper proposes three new information measures for individual sequences and clarifies their properties. Our new information measures are called as the non-overlapping max-entropy, the overlapping smooth max-entropy, and the non-overlapping smooth max-entropy, respectively. These measures are related to the fixed-length coding of individual sequences. We investigate these measures, and show the following three properties: (1) The non-overlapping max-entropy coincides with the topological entropy. (2) The overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the Ziv-entropy. (3) When an individual sequence is drawn from an ergodic source, the overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the entropy rate of the source. Further, we apply these information measures to the fixed-length coding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023TAP0005/_p

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@ARTICLE{e107-a_3_393,

author={Tomohiko UYEMATSU, Tetsunao MATSUTA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Equivalences among Some Information Measures for Individual Sequences and Their Applications for Fixed-Length Coding Problems},

year={2024},

volume={E107-A},

number={3},

pages={393-403},

abstract={This paper proposes three new information measures for individual sequences and clarifies their properties. Our new information measures are called as the non-overlapping max-entropy, the overlapping smooth max-entropy, and the non-overlapping smooth max-entropy, respectively. These measures are related to the fixed-length coding of individual sequences. We investigate these measures, and show the following three properties: (1) The non-overlapping max-entropy coincides with the topological entropy. (2) The overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the Ziv-entropy. (3) When an individual sequence is drawn from an ergodic source, the overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the entropy rate of the source. Further, we apply these information measures to the fixed-length coding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.},

keywords={},

doi={10.1587/transfun.2023TAP0005},

ISSN={1745-1337},

month={March},}

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TY - JOUR

TI - Equivalences among Some Information Measures for Individual Sequences and Their Applications for Fixed-Length Coding Problems

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 393

EP - 403

AU - Tomohiko UYEMATSU

AU - Tetsunao MATSUTA

PY - 2024

DO - 10.1587/transfun.2023TAP0005

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E107-A

IS - 3

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - March 2024

AB - This paper proposes three new information measures for individual sequences and clarifies their properties. Our new information measures are called as the non-overlapping max-entropy, the overlapping smooth max-entropy, and the non-overlapping smooth max-entropy, respectively. These measures are related to the fixed-length coding of individual sequences. We investigate these measures, and show the following three properties: (1) The non-overlapping max-entropy coincides with the topological entropy. (2) The overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the Ziv-entropy. (3) When an individual sequence is drawn from an ergodic source, the overlapping smooth max-entropy and the non-overlapping smooth max-entropy coincide with the entropy rate of the source. Further, we apply these information measures to the fixed-length coding of individual sequences, and propose some new universal coding schemes which are asymptotically optimum.

ER -