Minimum distortion quantizers

Abstract

The well-known algorithm of Max is used to determine the minimum distortion quantizers for normal, two-sided exponential, and specialized two-sided gamma input distributions and for mean-square, magnitude, and relative magnitude error distortion criteria. The optimum equally-spaced and unequally-spaced quantizers are found, with the resulting quantizer distortion and entropy. The quantizers, and the quantizers with entropy coding, are compared to the rate distortion bounds for mean-square and magnitude error.