A Lagrangian formulation of Zador's entropy-constrained quantization theorem
Richard A. Gray, Tamás Linder, Jia Ming Li · IEEE Transactions on Information Theory · 2002
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.