Quantization for uniform distributions on Sierpi\'nski carpets with strong separation condition
Doğan Çömez, Mrinal Kanti Roychowdhury · arXiv (Cornell University) · 2015
Let $P$ be a Borel probability measure on $\mathbb R^2$ supported by the Sierpi\'nski carpet generated by a set of four contractive similarity mappings satisfying the strong separation condition. For this probability measure, we determine the optimal sets of $n$-means and the $n$th quantization errors for all $n\geq 2$. In addition, it is shown that though the quantization dimension of the measure $P$ is known, the quantization coefficient for $P$ does not exist.