Bounds and Asymptotes for the Performance of Multivariate Quantizers.

摘要

The author discusses the minimization of a measure of the error introduced by a quantizer Q having a fixed number K of quantizing regions by varying the shapes of the regions. The results require that the probability measure mu have compact support, vanishing outside some cube in E sup n. However one does not need the absolute continuity of mu or the boundedness of its density f; one obtains firm lower bounds which are also estimates asymptotic in K, there are no unknown constants for general N and r, and the results extend to r = 0 and r = infinity.