Title :
A Lagrangian formulation of Zador´s entropy-constrained quantization theorem
Author :
Gray, Robert M. ; Linder, Tamás ; Li, Jia
Author_Institution :
Dept. of Electr. Eng., Stanford Univ., CA, USA
fDate :
3/1/2002 12:00:00 AM
Abstract :
Zador´s (1963, 1966) classic result for the asymptotic high-rate behavior of entropy-constrained vector quantization is recast in a Lagrangian form which better matches the Lloyd algorithm used to optimize such quantizers. The equivalence of the two formulations is shown and the result is proved for source distributions that are absolutely continuous with respect to the Lebesgue measure which satisfy an entropy condition, thereby generalizing the conditions stated by Zador under which the result holds
Keywords :
entropy; rate distortion theory; statistical analysis; vector quantisation; Lagrangian formulation; Lebesgue measure; VQ; Zador´s entropy-constrained quantization theorem; asymptotic high-rate behavior; average distortion; differential entropy; entropy-constrained vector quantization; rate allocation; source distributions; Algorithm design and analysis; Councils; Decoding; Distortion measurement; Entropy; History; Lagrangian functions; Network address translation; Rate distortion theory; Vector quantization;
Journal_Title :
Information Theory, IEEE Transactions on
