The quantization error of self-similar distributions
Klaus Pötzelberger · Mathematical Proceedings of the Cambridge Philosophical Society · 2004
We prove results on the asymptotic behavior of the quantization error for self-similar distributions $P$ when $n$ , the number of prototypes, goes to infinity. In particular, we show that the suitably scaled quantization error converges, if $P$ is nonarithmetic and that it is asymptotically periodic in the arithmetic case. The results hold also for distributions that are absolutely continuous with respect to a self-similar distribution.