Optimum Quantizer Design Using a Fixed-Point Algorithm

Abstract

A fixed-point algorithm has been used to obtain the parameters (i.e., decision and representative levels) of an “optimum” quantizer that minimizes a quite general distortion measure, subject to an entropy constraint on its output. Construction of the algorithm starts with a point-to-set mapping whose fixed point satisfies the well-known Karush-Kuhn-Tucker conditions necessary for a local extremum. A computer program is then used to determine a fixed point of this mapping. Several examples are solved, and correspondence with the existing results in the literature is pointed out. Finally, as conjectured, the growth of the computations as a function of dimensionality n (n: number of representative levels) is found to be of the form a · n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> where a is a positive constant and 1.5 ≦ b ≦ 2.0.