Optimum Quantizer Design Using a Fixed-Point Algorithm

Simple quantization 1 - 3 has been and continues to be a popular method of digitizing analog signals. The relative ease with which quantizers can be implemented in hardware and their near optimum performance has made them withstand the challenge from several new coding schemes. 4-6 Universal use of quantizers has naturally spurred a significant activity in optimizing their performance, some of which is summarized in the next few paragraphs. Our objective in this paper is to show how the problem of obtaining the parameters of an optimum quantizer can be converted to the problem of obtaining fixed points of a suitably constructed mapping and then to use a fixed-point algorithm to solve the problem numerically. Quantizers have been optimized based on several criteria. In order to discuss these in relation to the problem considered in this paper, we describe the basic quantizer equations. Given a scalar random variable T with probability density p(t), a quantizer Q is a map Q(t) = !/, whenever Xi ^ t