Voronoi regions

The first time, I came across Voronoi regions is in the context of Maximum likelihood decoding of symbol detection in digital communication. For equally likely transmitted constellation, in additive white Gaussian noise channel, the optimum symbol detection follows the simple voronoi partitioning (voronoi regions based on the a posteriori probability in the more general case, or based on the maximum likelihood criteria when the a posteriori probabilities are unknown). If the noisy received symbol (signal) falls into the well defined voronoi region, the symbol is decoded as the transmitted symbol present in the voronoi region. Of course, each voronoi region would have one symbol from the transmitted constellation.


Voronoi regions are applied much widely in applied mathematics and topology.