Asymptotic quantization error of continuous signals and the quantization dimension

Authors:
P. Zador
Affiliations:
-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

Extensions of the limiting qnanfizafion error formula of Bennet are proved. These are of the formD_{s,k}(N,F)=N^{-beta}B, whereNis the number of output levels,D_{s,k}(N,F)is thesth moment of the metric distance between quantizer input and output,beta,B>0,k=s/betais the signal space dimension, andFis the signal distribution. If a suitably well-behavedk-dimensional signal densityf(x)exists,B=b_{s,k}[int f^{rho}(x)dx]^{1/ rho},rho=k/(s+k), andb_{s,k}does not depend onf. Fork=1,s=2this reduces to Bennett's formula. IfFis the Cantor distribution on[0,1],0