Optimal Quantization of the Rayleigh Probability Distribution

We have derived an efficient and general algorithm for optimal quantization and applied it to the important, but neglected Rayleigh random variable. The optimal quantization range and output levels for the distortion criterion of minimum mean squared error have been calculated and tabulated for numbers of output levels from 1 to 64. We also compute and report the corresponding distortions and output entropies. For the sake of comparison, we also calculate and tabulate level spacings, minimum errors, and entropies for the optimal uniform (equal step size) quantization of the Rayleigh density. Distortion-rate curves are presented for uncoded and entropy coded quantizer outputs and compared with the distortion-rate function. We judge that these results will be useful to workers in the fields of optical holography, image processing, and communications.