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New NonAsymptotic Bounds on Numbers of Codewords for the FixedLength Lossy Compression
Tetsunao MATSUTA Tomohiko UYEMATSU
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E99A
No.12
pp.21162129 Publication Date: 2016/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E99.A.2116
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Source Coding and Data Compression Keyword: finite blocklength, nonasymptotic bound, ratedistortion function, source coding,
Full Text: PDF>>
Summary:
In this paper, we deal with the fixedlength lossy compression, where a fixedlength sequence emitted from the information source is encoded into a codeword, and the source sequence is reproduced from the codeword with a certain distortion. We give lower and upper bounds on the minimum number of codewords such that the probability of exceeding a given distortion level is less than a given probability. These bounds are characterized by using the αmutual information of order infinity. Further, for i.i.d. binary sources, we provide numerical examples of tight upper bounds which are computable in polynomial time in the blocklength.

