On the whiteness of high-resolution quantization errors

A common belief in quantization theory says that the quantization noise process resulting from uniform scalar quantization of a correlated discrete-time process tends to be white in the limit of small distortion ("high resolution"). A rule of thumb for this property to hold is that the source samples have a "smooth" joint distribution. We give a precise statement of this property, and generalize it to nonuniform quantization and to vector quantization. We show that the quantization errors resulting from independent quantizations of dependent real random variables become asymptotically uncorrelated (although not necessarily statistically independent) if the joint Fisher information (FI) under translation of the two variables is finite and the quantization cells shrink uniformly as the distortion tends to zero.