Dithering in lattice quantization

We study error statistics of lattice quantization with and without vector dithering. As in the scalar case, we distinguish between subtractive and nonsubtractive dithering. We derive general expressions for appropriate error statistics in both cases. In subtractive dithering, we can achieve statistical independence of the error vector from the input vector by appropriate choice of the dither vector. The resulting error is determined by the lattice and there exist optimum lattices that minimize the total mean square error. We give a necessary condition on such a lattice. In nonsubtractive dithering, the moments of the error vector can be made independent of the input. The resulting error depends on both the lattice and the dither vector. We indicate methods for generating suitable dither vectors for each scheme.