Universal Lossy Coding for Individual Sequences Based on Complexity Functions

Shigeaki KUZUOKA; Tomohiko UYEMATSU

doi:10.1093/ietfec/e90-a.2.491

Universal Lossy Coding for Individual Sequences Based on Complexity Functions

Shigeaki KUZUOKA, Tomohiko UYEMATSU

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This paper investigates the fixed-rate and fixed-distortion lossy coding problems of individual sequences subject to the subadditive distortion measure. The fixed-rate and fixed-distortion universal lossy coding schemes based on the complexity of the sequence are proposed. The obtained coding theorems reveal that the optimal distortion (resp. rate) attainable by the fixed-rate (resp. fixed-distortion) lossy coding is equal to the optimal average distortion (resp. rate) with respect to the overlapping empirical distribution of the given sequence. Some connections with the lossy coding problem of ergodic sources are also investigated.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.2 pp.491-503

Publication Date: 2007/02/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e90-a.2.491

Type of Manuscript: PAPER

Category: Information Theory

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Shigeaki KUZUOKA, Tomohiko UYEMATSU, "Universal Lossy Coding for Individual Sequences Based on Complexity Functions" in IEICE TRANSACTIONS on Fundamentals, vol. E90-A, no. 2, pp. 491-503, February 2007, doi: 10.1093/ietfec/e90-a.2.491.
Abstract: This paper investigates the fixed-rate and fixed-distortion lossy coding problems of individual sequences subject to the subadditive distortion measure. The fixed-rate and fixed-distortion universal lossy coding schemes based on the complexity of the sequence are proposed. The obtained coding theorems reveal that the optimal distortion (resp. rate) attainable by the fixed-rate (resp. fixed-distortion) lossy coding is equal to the optimal average distortion (resp. rate) with respect to the overlapping empirical distribution of the given sequence. Some connections with the lossy coding problem of ergodic sources are also investigated.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.2.491/_p

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@ARTICLE{e90-a_2_491,
author={Shigeaki KUZUOKA, Tomohiko UYEMATSU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Universal Lossy Coding for Individual Sequences Based on Complexity Functions},
year={2007},
volume={E90-A},
number={2},
pages={491-503},
abstract={This paper investigates the fixed-rate and fixed-distortion lossy coding problems of individual sequences subject to the subadditive distortion measure. The fixed-rate and fixed-distortion universal lossy coding schemes based on the complexity of the sequence are proposed. The obtained coding theorems reveal that the optimal distortion (resp. rate) attainable by the fixed-rate (resp. fixed-distortion) lossy coding is equal to the optimal average distortion (resp. rate) with respect to the overlapping empirical distribution of the given sequence. Some connections with the lossy coding problem of ergodic sources are also investigated.},
keywords={},
doi={10.1093/ietfec/e90-a.2.491},
ISSN={1745-1337},
month={February},}

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TY - JOUR
TI - Universal Lossy Coding for Individual Sequences Based on Complexity Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 491
EP - 503
AU - Shigeaki KUZUOKA
AU - Tomohiko UYEMATSU
PY - 2007
DO - 10.1093/ietfec/e90-a.2.491
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2007
AB - This paper investigates the fixed-rate and fixed-distortion lossy coding problems of individual sequences subject to the subadditive distortion measure. The fixed-rate and fixed-distortion universal lossy coding schemes based on the complexity of the sequence are proposed. The obtained coding theorems reveal that the optimal distortion (resp. rate) attainable by the fixed-rate (resp. fixed-distortion) lossy coding is equal to the optimal average distortion (resp. rate) with respect to the overlapping empirical distribution of the given sequence. Some connections with the lossy coding problem of ergodic sources are also investigated.
ER -