Vector Quantization with Error Uniformly Distributed over an Arbitrary Set

For uniform scalar quantization, the error distribution is approximately a uniform distribution over an interval (which is also a 1-dimensional ball). Nevertheless, for lattice vector quantization, the error distribution is uniform not over a ball, but over the basic cell of the quantization lattice. In this paper, we construct vector quantizers where the error is uniform over the n-ball, or any other prescribed set. We then prove bounds on the entropy of the quantized signals.