Piecewise uniform vector quantizers

The companding model for quantizer design and analysis has been frequently used in various instances. However, if the signal to be quantized is a vector, then the optimum companding system can be designed for only a limited number of distributions. On the other hand, piecewise linear companders can be designed for any signal density, generating quantizers that are uniform on each region of the compander. These systems, while not optimal, can have performances which are close to the optimum, and their analysis and implementation can be simpler than those of optimal systems. In this paper we analyze piecewise linear companders for asymptotic multidimensional quantization, and we suggest methods for their design.