2016/04/14 by Doğan Çömez, Comez, Dogan, Mrinal Kanti Roychowdhury +1
Computer Science · #28A80 #60Exx #94A34 #Advanced Data Compression Techniques #Dynamical Systems (math.DS) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1604.04261
openalex publication_date 2016/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of affine transformations \Sij\ on \mathbb R2 with associated probabilities \pij\ such that pij>0 for all i, j∈ \mathbb N and ∑i, j=1^∞ pij=1. For such a probability measure P, the optimal sets of n-means and the nth quantization error are calculated for every natural number n. It is shown that the distribution of such a probability measure is the same as that of the direct product of the Cantor distribution. In addition, it is proved that the quantization dimension D(P) exists and is finite; whereas, the D(P)-dimensional quantization coefficient does not exist, and the D(P)-dimensional lower and the upper quantization coefficients lie in the closed interval [(1)/(12), (5)/(4)].