On the Wyner-Ziv Source Coding Problem with Unknown Delay

Tetsunao MATSUTA; Tomohiko UYEMATSU

doi:10.1587/transfun.E97.A.2288

On the Wyner-Ziv Source Coding Problem with Unknown Delay

Tetsunao MATSUTA, Tomohiko UYEMATSU

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In this paper, we consider the lossy source coding problem with delayed side information at the decoder. We assume that delay is unknown but the maximum of delay is known to the encoder and the decoder, where we allow the maximum of delay to change with the block length. In this coding problem, we show an upper bound and a lower bound of the rate-distortion (RD) function, where the RD function is the infimum of rates of codes in which the distortion between the source sequence and the reproduction sequence satisfies a certain distortion level. We also clarify that the upper bound coincides with the lower bound when maximums of delay per block length converge to a constant. Then, we give a necessary and sufficient condition in which the RD function is equal to that for the case without delay. Furthermore, we give an example of a source which does not satisfy this necessary and sufficient condition.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.12 pp.2288-2299

Publication Date: 2014/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E97.A.2288

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

Category: Shannon Theory

Authors

Tetsunao MATSUTA
Tokyo Institute of Technology
Tomohiko UYEMATSU
Tokyo Institute of Technology

Keyword

delay, rate-distortion function, side information, source coding

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Tetsunao MATSUTA, Tomohiko UYEMATSU, "On the Wyner-Ziv Source Coding Problem with Unknown Delay" in IEICE TRANSACTIONS on Fundamentals, vol. E97-A, no. 12, pp. 2288-2299, December 2014, doi: 10.1587/transfun.E97.A.2288.
Abstract: In this paper, we consider the lossy source coding problem with delayed side information at the decoder. We assume that delay is unknown but the maximum of delay is known to the encoder and the decoder, where we allow the maximum of delay to change with the block length. In this coding problem, we show an upper bound and a lower bound of the rate-distortion (RD) function, where the RD function is the infimum of rates of codes in which the distortion between the source sequence and the reproduction sequence satisfies a certain distortion level. We also clarify that the upper bound coincides with the lower bound when maximums of delay per block length converge to a constant. Then, we give a necessary and sufficient condition in which the RD function is equal to that for the case without delay. Furthermore, we give an example of a source which does not satisfy this necessary and sufficient condition.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.2288/_p

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@ARTICLE{e97-a_12_2288,
author={Tetsunao MATSUTA, Tomohiko UYEMATSU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Wyner-Ziv Source Coding Problem with Unknown Delay},
year={2014},
volume={E97-A},
number={12},
pages={2288-2299},
abstract={In this paper, we consider the lossy source coding problem with delayed side information at the decoder. We assume that delay is unknown but the maximum of delay is known to the encoder and the decoder, where we allow the maximum of delay to change with the block length. In this coding problem, we show an upper bound and a lower bound of the rate-distortion (RD) function, where the RD function is the infimum of rates of codes in which the distortion between the source sequence and the reproduction sequence satisfies a certain distortion level. We also clarify that the upper bound coincides with the lower bound when maximums of delay per block length converge to a constant. Then, we give a necessary and sufficient condition in which the RD function is equal to that for the case without delay. Furthermore, we give an example of a source which does not satisfy this necessary and sufficient condition.},
keywords={},
doi={10.1587/transfun.E97.A.2288},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - On the Wyner-Ziv Source Coding Problem with Unknown Delay
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2288
EP - 2299
AU - Tetsunao MATSUTA
AU - Tomohiko UYEMATSU
PY - 2014
DO - 10.1587/transfun.E97.A.2288
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2014
AB - In this paper, we consider the lossy source coding problem with delayed side information at the decoder. We assume that delay is unknown but the maximum of delay is known to the encoder and the decoder, where we allow the maximum of delay to change with the block length. In this coding problem, we show an upper bound and a lower bound of the rate-distortion (RD) function, where the RD function is the infimum of rates of codes in which the distortion between the source sequence and the reproduction sequence satisfies a certain distortion level. We also clarify that the upper bound coincides with the lower bound when maximums of delay per block length converge to a constant. Then, we give a necessary and sufficient condition in which the RD function is equal to that for the case without delay. Furthermore, we give an example of a source which does not satisfy this necessary and sufficient condition.
ER -