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Distortion-rate theory for individual sequences

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For every individual infinite sequenceuwe define a distortion-rate functiond(R|u)which is shown to be an asymptotically attainable lower bound on the distortion that can be achieved foruby any finite-state encoder which operates at a fixed output information rateR. This is done by means of a coding theorem and its converse. No probabilistic characterization ofuis 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 capacityCis also investigated. It is shown that, for every given sequenceuand any finite-state encoder, the average distortion with respect to the channel statistics is lower bounded byd(C|u). Furthermored(C|u)is asymptotically attainable.

Published in:

Information Theory, IEEE Transactions on  (Volume:26 ,  Issue: 2 )

Date of Publication:

Mar 1980

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