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Optimal quantization for the one-dimensional uniform distribution with Rényi-$$\alpha$$-entropy constraints. (English) Zbl 1187.94018
Summary: We establish the optimal quantization problem for probabilities under constrained Rényi-$$\alpha$$-entropy of the quantizers. We determine the optimal quantizers and the optimal quantization error of one-dimensional uniform distributions including the known special cases $$\alpha = 0$$ (restricted codebook size) and $$\alpha = 1$$ (restricted Shannon entropy).

##### MSC:
 94A17 Measures of information, entropy 62H30 Classification and discrimination; cluster analysis (statistical aspects) 94A29 Source coding
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##### References:
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