TY - INPR A1 - Kreitmeier, Wolfgang T1 - Error bounds for high-resolution quantization with Rényi - α - entropy constraints N2 - We consider the problem of optimal quantization with norm exponent r > 0 for Borel probabilities on Rd under constrained Rényi-α-entropy of the quantizers. If the bound on the entropy becomes large, then sharp asymptotics for the optimal quantization error are well-known in the special cases α = 0 (memory-constrained quantization) and α = 1 (Shannon-entropy-constrained quantization). In this paper we determine sharp asymptotics for the optimal quantization error under large entropy bound with entropy parameter α ∈ [1+r/d, ∞]. For α ∈ [0,1+r/d[ we specify the asymptotical order of the optimal quantization error under large entropy bound. The optimal quantization error decays exponentially fast with the entropy bound and the exact decay rate is determined for all α ∈ [0, ∞]. KW - Maßtheorie KW - Quantisierung KW - Vektorquantisierung KW - Entropie KW - Vector quantization KW - high-resolution quantization KW - Rényi-α-entropy KW - approximation of probabilities Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:739-opus-16647 ER -