When is an optimal transform coder orthonormal?

We consider optimum Transform coding. The objective is to minimize the distortion variance by selecting an op- timum transform matrix and bit allocation among the sub- band signals. Under an asymptotic expression for the quan- tizer distortion function it is known that the optimum trans- form can be chosen to be orthonormal and regardless of the precise allocated bit values. In this paper we have given suf- ficient conditions on the quantizer distortion function that ensure this property.