Vanishing distortion and shrinking cells
Andrew B. Nobel · IEEE Transactions on Information Theory · 1996
We establish an asymptotic connection between vanishing rth-power distortion and shrinking cell diameters for vector quantizers with convex cells. As a consequence, a number of shrinking cell conditions may be easily verified by showing that the quantizers in question have distortion tending to zero. This also plays an important role in the asymptotic analysis of a common greedy growing scheme for tree-structured vector quantizers.