NDLI: The redundancy of source coding with a fidelity criterion. 1. Known statistics

Content Provider	IEEE Xplore Digital Library
Author	Zhang, Z. Yang, E.-h. Wei, V.K.
Copyright Year	1963
Abstract	The problem of redundancy of source coding with respect to a fidelity criterion is considered. For any fixed rate R>0 and any memoryless source with finite source and reproduction alphabets and a common distribution p, the nth-order distortion redundancy D/sub n/(R) of fixed-rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate R and the distortion rate function d(p,R) of the source p. It is demonstrated that for sufficiently large n, D/sub n/(R) is equal to -(/spl part///spl part/R)d(p,R) ln n/2n+o(ln n/n), where (/spl part///spl part/R)d(p,R) is the partial derivative of d(p,R) evaluated at R and assumed to exist. For any fixed distortion level d>0 and any memoryless source p, the nth-order rate redundancy R/sub n/(d) of coding at fixed distortion level d (or by using d-semifaithful codes) is defined as the minimum of the difference between the expected rate per symbol of any d-semifaithful code of length n and the rate-distortion function R(p,d) of p evaluated at d. It is proved that for sufficiently large n, R/sub n/(d) is upper-bounded by ln n/n+o(ln n/n) and lower-bounded by In n/2n+o(In n/n). As a by-product, the lower bound of R/sub n/(d) derived in this paper gives a positive answer to a conjecture proposed by Yu and Speed (1993).
Sponsorship	IEEE Information Theory Society
Starting Page	71
Ending Page	91
Page Count	21
File Size	1701667
File Format	PDF
ISSN	00189448
Volume Number	43
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1997-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Source coding Statistics Rate-distortion Entropy Block codes Rate distortion theory Length measurement Distortion measurement Statistical distributions Mutual information
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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