Lattice quantization noise revisited

Dithered quantization is widely used in signal processing and coding due to its many desirable properties in theory and in practice. In this paper, we show that dither is unnecessary for Gaussian sources when the flatness factor of the quantization lattice is small. This means that the quantization noise behaves much like that in dithered quantization. In particular, it tends to be uniformly distributed over any fundamental region of the lattice and be uncorrelated with the signal; further, for optimum lattice quantizers, it approaches the rate-distortion bound of Gaussian sources with minimum mean-square error (MMSE) estimation.