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Variable-rate source coding theorems for stationary nonergodic sources

Effros, M. and Chou, P. A. and Gray, R. M. (1994) Variable-rate source coding theorems for stationary nonergodic sources. IEEE Transactions on Information Theory, 40 (6). pp. 1920-1925. ISSN 0018-9448. doi:10.1109/18.340466.

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For a stationary ergodic source, the source coding theorem and its converse imply that the optimal performance theoretically achievable by a fixed-rate or variable-rate block quantizer is equal to the distortion-rate function, which is defined as the infimum of an expected distortion subject to a mutual information constraint. For a stationary nonergodic source, however, the. Distortion-rate function cannot in general be achieved arbitrarily closely by a fixed-rate block code. We show, though, that for any stationary nonergodic source with a Polish alphabet, the distortion-rate function can be achieved arbitrarily closely by a variable-rate block code. We also show that the distortion-rate function of a stationary nonergodic source has a decomposition as the average of the distortion-rate functions of the source's stationary ergodic components, where the average is taken over points on the component distortion-rate functions having the same slope. These results extend previously known results for finite alphabets.

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Additional Information:“© 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received July 6, 1993; revised March 31, 1994. This material is based upon work partially supported by the National Science Foundation under an NSF Graduate Fellowship, by a grant from The Center for Telecommunications at Stanford, and by an AT & T Ph.D. Scholarship. This paper was presented in part at the 1994 IEEE International Symposium on Information Theory, Trondheim, Norway.
Subject Keywords:Source coding theorems, stationary nonergodic sources, distortion-rate function, source coding theory
Issue or Number:6
Record Number:CaltechAUTHORS:EFFieeetit94b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:556
Deposited By: Archive Administrator
Deposited On:26 Jul 2005
Last Modified:08 Nov 2021 19:03

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