Upper bounds to the asymptotic performance of block quantizers

Upper bounds to the asymptotic performance of block quantizers with difference distortion measures are derived. In many eases, these upper bounds approach known lower bounds as the block length of the quantizer approaches infinity. A condition for the optimal point density function of the output levels is derived. It is shown to particularize to a known result of Gersho. The behavior of the bounds for large block lengths is investigated.