ON LATTICE QUANTIZATION NOISE

We present several results regarding the properties of a random vector , uniformly distributed over a lattice cell, This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels, We fin d that for the optimal lattice quantizers this noise is wide-sense-sta tionary and white. Any desirable noise spectra may be realized by an a ppropriate linear transformation (''shaping'') of a lattice quantizer. As the dimension increases, the normalized second moment of the optim al lattice quantizer goes to 1/2 pi e, and consequently the quantizati on noise approaches a white Gaussian process in the divergence sense, In entropy-coded dithered quantization, which can be modeled accuratel y as passing the source through an additive noise channel, this limit behavior implies that for large lattice dimension both the error and t he bit rate approach the error and the information rate of an Additive White Gaussian Noise (AWGN) channel.