Solution of the Lloyd-Max quantizer parameters by the method of successive substitution

Abstract

The method of successive substitution is shown applicable to solve for the classical minimum distortion quantizer parameters. The method is self converging and parameters can be calculated to any desired accuracy. The minimum distortion quantizer parameters, as well as parameters based on other criterion such as quantizers for signal detection, minimum risk quantizers and quantizers for LMMS estimation can be solved by Max's trial and error technique. There are also many other approximation methods to calculate the quantizer parameters. This report applies the method of successive substitution and its modifications to solve for the Lloyd-Max quantizer parameters. It is more accurate and computationally more efficient than the previously reported methods. It is shown to easily generate 7 bit (128 level) optimum quantization. The Lloyd-Max minimum mean square distortion quantizer problem deals with transforming a random variable X of differentiable probability density function f(x) into the N-level discrete random variable Y