Universal Lossy Coding for Individual Sequences Based on Complexity Functions

Shigeaki KUZUOKA
Tomohiko UYEMATSU

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A    No.2    pp.491-503
Publication Date: 2007/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.2.491
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
complexity,  individual sequence,  lossy coding,  universal coding,  

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Summary: 
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.

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