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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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