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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 variableXusing anN-level quantizerQto minimize the expected distortionE rho(|X-Q(X))I), where the error weighting functionrhois convex, strictly increasing and continuously differentiable. It is shown that ifXhas a log-concave density, then there exists a unique locally optimal quantizerQ astand Lloyd's Method I may be used to findQ ast. Trushkin had earlier shown this result for the error weighting functionsrho (t) equiv tandrho(t) euiv t^{2}.

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