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Upper bounds are presented for the difference in entropy between that of a uniform scalar quantizer and that of any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -dimensional quantizer. The bounds are universal in the sense that they suit every input density and every value of distortion. Bounds were found for some common distortion criteria.
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M. Gutman (1987) studied this question.
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