White Noise Hypothesis for Uniform Quantization Errors

The white noise hypothesis (WNH) assumes that in the uniform pulse code modulation (PCM) quantization scheme the errors in individual channels behave like white noise; i.e., they are independent and identically distributed random variables. The WNH is key to estimating the mean square quantization error (MSE). But is the WNH valid? In this paper we take a close look at the WNH. We show that in a redundant system the errors from individual channels can never be independent. Thus to an extent the WNH is invalid. Our numerical experiments also indicate that with coarse quantization the WNH is far from valid. However, as the main result of this paper we show that with fine quantizations the WNH is essentially valid in that the errors from individual channels become asymptotically pairwise independent, each uniformly distributed in $[-\Delta/2, \Delta/2)$, where Δ denotes the stepsize of the quantization.