Suboptimality of the Karhunen-Loeve transform for fixed-rate transform coding

An open problem in source coding theory has been whether the Karhunen-Loeve transform (KLT) is optimal for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. Huang and Schultheiss (1963) proved that for a Gaussian source the KLT is mean squared optimal in the limit of high quantizer resolution. It is often assumed and stated in the literature that the KLT is also optimal in general for nonGaussian sources. We disprove such assertions by demonstrating that the KLT is not optimal for certain nearly bimodal Gaussian and uniform sources. In addition, we show the unusual result that for vector sources with independent identically distributed Laplacian components, the distortion resulting from scalar quantizing the components can be reduced by including an orthogonal transform that adds intercomponent dependency.