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Vector Quantization with Error Uniformly Distributed over an Arbitrary Set. (arXiv:2305.06788v1 [cs.IT])

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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.

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