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

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1 Author(s)

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} .

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IEEE Transactions on Information Theory  (Volume:29 ,  Issue: 1 )