مرکز منطقه ای اطلاع رساني علوم و فناوري - Uniqueness of locally optimal quantizer for log-concave density and convex error weighting function

DocumentCode :

935971

Title :

Uniqueness of locally optimal quantizer for log-concave density and convex error weighting function

Author :

Kieffer, John C.

Volume :

Issue :

fYear :

1983

fDate :

1/1/1983 12:00:00 AM

Firstpage :

Lastpage :

Abstract :

It is desired to encode a random variable $X$ using an $N$ -level quantizer $Q$ to minimize the expected distortion $E \\rho(|X-Q(X))I)$ , where the error weighting function $\\rho$ is convex, strictly increasing and continuously differentiable. It is shown that if $X$ has a log-concave density, then there exists a unique locally optimal quantizer $Q \\ast$ and Lloyd\´s Method I may be used to find $Q \\ast$ . Trushkin had earlier shown this result for the error weighting functions $\\rho (t) \\equiv t$ and $\\rho(t) euiv t^{2}$ .