Vector Quantization With Error Uniformly Distributed Over An Arbitrary Set
Chih Wei Ling, Cheuk Ting Li . 2023 IEEE International Symposium on Information Theory (ISIT) 2023 – 5 citations
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 with periodic properties, where the error is uniformly distributed over the n-ball, or any other prescribed set. We then prove upper and lower bounds on the entropy of the quantized signals. We also discuss how our construction can be applied to give a randomized quantization scheme with a nonuniform error distribution.