Optimum Quantization for Minimum Distortion

Abstract

This paper treats the problem of optimal selection of data quantization levels for minimum error. No assumptions are made regarding the underlying statistics of the process to be quantized. A finite precursor sample of the data is analyzed to infer the underlying distribution. Selection of optimum quantization levels can then be related to the generation of an optimum histogram for the data record. The optimum histogram is obtained by a dynamic programming approach for both least mean square error and minimum Chebychev error criteria. Transmitted data can then be quantized according to levels specified by the histogram. The process can be repeated periodically either with a new data sample, if the underlying process is nonstationary, or performed on the accumulated record in the stationary case.