The design of two-dimensional quantizers using prequantization

The theoretical advantages of two-dimensional quantization over univariate quantization have been studied in the literature. However, in many cases there is no known implementation for the two-dimensional quantizer that can operate in real time. A new approach to the design of two-dimensional quantizers is presented. This technique, called prequantization, is used to design two-dimensional quantizers that operate in real time. The importance of prequantization is demonstrated by the design of the optimum uniform two-dimensional (hexagonal) quantizer. Additional examples are given to illustrate the flexibility of this design approach.