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 -