# Optimal quantization for the one-dimensional uniform distribution with Rényi-α-entropy constraints

Wolfgang Kreitmeier

# Abstract:

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).

# Keywords:

optimal quantization, uniform distribution, Rényi-$&alpha;$-entropy

# Classification:

60Exx, 62H30, 94A17, 94A29