On lattice quantization noise

Presents several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise associated with dithered lattice quantization, and at high resolution it is the noise generated in regular lattice quantization of “smooth” sources. The authors find that the noise associated with the optimal lattice quantizers is wide-sense stationary and white. Any desirable noise spectra may be realized by an appropriate linear transformation (“shaping”) of a lattice quantizer. As the dimension increases, the normalized second moment of the optimal lattice quantizer goes to 1/2πe, and consequently the quantization noise approaches a white Gaussian process. Actually, in entropy coded dithered quantization where the quantization procedure can be modeled as an additive noise channel, this limit behavior implies that both the asymptotic MSE distortion and the mutual-information between input and output of the quantization channel, approaches the MSE and the mutual-information between input and output of an additive white Gaussian noise (AWGN) channel