Some results on robust data quantization

A minimax approach to designing quantizers which are robust over classes of input statistics is considered. Several recent results pertaining to this problem are surveyed. These results include an asymptotic (as the number of levels approaches infinity) design formulation in which minimax distortion quantizers are derived on the basis of the so-called "companding" approximations. Some new results for this problem are also presented, including one result which demonstrates a possible shortcoming of this asymptotic approach. In particular it is demonstrated that the maximization and limiting operations cannot generally be interchanged in this problem because of its discrete nature.