Vector Quantization with Error Uniformly Distributed over an Arbitrary Set

05/11/2023

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by   Chih Wei Ling, et al.

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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.