Fast quantizing and decoding and algorithms for lattice quantizers and codes

For each of the lattices
A_{n}(n \geq 1), D_{n}(n \geq 2), E_{6}, E_{7}, E_{8}
, and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point. If these lattices are used for vector quantizing of uniformly distributed data, the algorithm finds the minimum distortion lattice point. If the lattices are used as codes for a Gaussian channel, the algorithm performs maximum likelihood decoding.