A Lagrangian formulation of Zador's entropy-constrained quantization theorem

Robert M. Gray; Tamás Linder; Jia Li

doi:10.1109/18.986007

A Lagrangian formulation of Zador's entropy-constrained quantization theorem

Robert M. Gray
, Tamás Linder
, Jia Li

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

A Lagrangian formulation of Zador's entropy-constrained quantization theorem was presented. Zador's classic result for the asymptotic high-rate behavior of entropy-constrained vector quantization was recasted in a Lagrangian form which better matches the Lloyd algorithm used to optimize such quantizers. The result is proved for source distributions that are absolutely continuous with respect to the Lebesgue measure which satisfy an entropy condition.

Original language	English (US)
Pages (from-to)	695-707
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	48
Issue number	3
DOIs	https://doi.org/10.1109/18.986007
State	Published - Mar 2002

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/18.986007

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title = "A Lagrangian formulation of Zador's entropy-constrained quantization theorem",

abstract = "A Lagrangian formulation of Zador's entropy-constrained quantization theorem was presented. Zador's classic result for the asymptotic high-rate behavior of entropy-constrained vector quantization was recasted in a Lagrangian form which better matches the Lloyd algorithm used to optimize such quantizers. The result is proved for source distributions that are absolutely continuous with respect to the Lebesgue measure which satisfy an entropy condition.",

author = "Gray, \{Robert M.\} and Tam{\'a}s Linder and Jia Li",

note = "Funding Information: Manuscript received May 10, 2001; revised September 28, 2001. This work was supported in part by the National Science Foundation under NSF Grants MIP-9706284-001 and CCR-0073050 and by the Natural Sciences and Engineering Research Council (NSERC) of Canada. R. M. Gray is with Information Systems Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA (e-mail: rmgray @stanford.edu). T. Linder is with the Department of Mathematics and Statistics, Queen{\textquoteright}s University, Kingston, ON K7L 3N6, Canada (e-mail: [email protected]). J. Li is with the Department of Statistics, The Pennsylvania State University, University Park, PA 16802 USA (e-mail: [email protected]). Communicated by P. A. Chou, Associate Editor for Source Coding. Publisher Item Identifier S 0018-9448(02)00632-6.",

year = "2002",

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doi = "10.1109/18.986007",

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AU - Linder, Tamás

AU - Li, Jia

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A Lagrangian formulation of Zador's entropy-constrained quantization theorem

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