Robust quantizers designed using the companding approximation

This paper considers the design of a quantizer when the probability distribution of the input signal is not known exactly. A robust (minimax) quantizer is derived which produces the largest possible guaranteed signal-to-noise ratio over a sizeable class of input distributions (all unimodal distributions with a known moment). A closed-form solution for the robust quantization levels is possible by using the companding approximation. In many instances, the robust quantizer guarantees a significantly higher signal-to-noise ratio than quantizers designed for the standard distributions (uniform, Gaussian, Laplace.) A similar approach is used to "robustify" the commonly used ??-law and A-law companders.