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Multidimensional asymptotic quantization theory with $r$th power distortion measures

TitleMultidimensional asymptotic quantization theory with $r$th power distortion measures
Publication TypeJournal Article
Year of Publication1982
AuthorsJames A. Bucklew, and Gary L. Wise
JournalInformation Theory, IEEE Transactions on
Volume28
Issue2
Pagination239 - 247
Abstract

Asymptotic properties of therth power distortion measure associated with quantized $ k $-dimensional random variables are considered. Subject only to a moment condition, it is shown that the infimum over all $ N $ level quantizers of the quantity $ N^{r/k} $ times the $ r $th power average distortion converges to a finite constant as $ N \rightarrow \infty $.