When is an optimal transform coder orthonormal?

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