DocumentCode :
931370
Title :
Distortion-rate theory for individual sequences
Author :
Ziv, Jacob
Volume :
26
Issue :
2
fYear :
1980
fDate :
3/1/1980 12:00:00 AM
Firstpage :
137
Lastpage :
143
Abstract :
For every individual infinite sequence u we define a distortion-rate function d(R|u) which is shown to be an asymptotically attainable lower bound on the distortion that can be achieved for u by any finite-state encoder which operates at a fixed output information rate R . This is done by means of a coding theorem and its converse. No probabilistic characterization of u is assumed. The coding theorem demonstrates the existence of {em universal} encoders which are asymptotically optimal for every infinite sequence over a given finite alphabet. The transmission of individual sequences via a noisy channel with a capacity C is also investigated. It is shown that, for every given sequence u and any finite-state encoder, the average distortion with respect to the channel statistics is lower bounded by d(C|u) . Furthermore d(C|u) is asymptotically attainable.
Keywords :
Rate-distortion theory; Source coding; Channel capacity; Codes; Data compression; Decoding; Delay; Distortion measurement; Entropy; Error analysis; Jacobian matrices; Statistics;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1980.1056164
Filename :
1056164
Link To Document :
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