Optimal quantizers for a nonuniform distribution on a Sierpinski carpet

2016/05/08 by Roychowdhury, Mrinal Kanti
#28A80 #60Exx #94A34 #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1605.02281

Abstract

The purpose of quantization for a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonuniform probability measure P on \mathbb R² which has support the Sierpiński carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered. For this probability measure, the optimal sets of n-means and the nth quantization errors are investigated for all n≥ 2.

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