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In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the rate-distortion region for general sources, where the rate-distortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2110-2124

- Publication Date
- 2018/12/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E101.A.2110

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

- Category
- Shannon theory

Tetsunao MATSUTA

Tokyo Institute of Technology

Tomohiko UYEMATSU

Tokyo Institute of Technology

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Tetsunao MATSUTA, Tomohiko UYEMATSU, "Non-Asymptotic Bounds and a General Formula for the Rate-Distortion Region of the Successive Refinement Problem" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2110-2124, December 2018, doi: 10.1587/transfun.E101.A.2110.

Abstract: In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the rate-distortion region for general sources, where the rate-distortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2110/_p

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@ARTICLE{e101-a_12_2110,

author={Tetsunao MATSUTA, Tomohiko UYEMATSU, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Non-Asymptotic Bounds and a General Formula for the Rate-Distortion Region of the Successive Refinement Problem},

year={2018},

volume={E101-A},

number={12},

pages={2110-2124},

abstract={In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the rate-distortion region for general sources, where the rate-distortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.},

keywords={},

doi={10.1587/transfun.E101.A.2110},

ISSN={1745-1337},

month={December},}

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TY - JOUR

TI - Non-Asymptotic Bounds and a General Formula for the Rate-Distortion Region of the Successive Refinement Problem

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2110

EP - 2124

AU - Tetsunao MATSUTA

AU - Tomohiko UYEMATSU

PY - 2018

DO - 10.1587/transfun.E101.A.2110

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E101-A

IS - 12

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - December 2018

AB - In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the rate-distortion region for general sources, where the rate-distortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.

ER -