1. A method for determining indications of the distances between a received eight-dimensional vector having four two-dimensional coordinates and each of sixteen non-overlapping subconstellations, comprising: (a) obtaining indications of distances between each of said two-dimensional coordinates of said received vector and a first set of points in a two-dimensional plane, and between each of said two-dimensional coordinates of said received vector and non-overlapping second, third, and fourth sets of points generated by ninety, one hundred eighty and two hundred seventy degree rotations of said first set of points, wherein each of said sixteen non-overlapping subconstellations is represented by a collection of sixteen representational four-coordinate vectors, wherein an i'th coordinate of one of said four-coordinate representational vectors represents one of said four non-overlapping sets of points in an i'th plane, and wherein for any representational four-coordinate vector representing a particular subconstellation, said representational vectors which represent one hundred and eighty degree rotations in a first and second two-dimensional coordinate and zero rotation in a third and fourth two-dimensional coordinate, zero rotation in said first and second two-dimensional coordinate and one hundred eighty degree rotation in said third and fourth two-dimensional coordinates, and one hundred eighty degree rotation in all said four two-dimensional coordinates are also representative of said particular subconstellation; (b) using said obtained indications of distance for said two-dimensional coordinates to find an indication of distance between a first four-dimensional vector consisting of the first two two-dimensional coordinates of said received eight-dimensional vector and each of sixteen four-dimensional sets of points represented by sixteen two-coordinate representational vectors wherein a first coordinate represents one of said nonoverlapping sets of points in a first two-dimensional plane and wherein a second coordinate represents one of said nonoverlapping sets of points in a second two dimensional plane, and obtaining by comparison the smaller of two distance indications in each of eight pairs of distance indications to obtain a first group of eight shorter distances, each pair comprising the distance indication between said first four-dimensional vector and a particular of said four-dimensional set of points and the distance indication between said first four-dimensional vector and a set of four-dimensional points which is a hundred-eighty degree rotation of said particular four-dimensional set of points; (c) using said obtained indications of distance for said two-dimensional coordinates to find an indication of distance between a second four-dimensional vector consisting of the second two two-dimensional coordinates of said received eight-dimensional vector and each of a second collection of sixteen four-dimensional sets of points represented by a second collection of sixteen two-coordinate representational vectors wherein a first coordinate of said second four-dimensional vector represents one of said nonoverlapping sets of points in a third two-dimensional plane and wherein a second coordinate of said four-dimensional vector represents one of said nonoverlapping sets of points in a fourth two-dimensional plane, and obtaining by comparison the smaller of two distance indications in each of a second group of eight pairs of distance indications to obtain a second group of eight shorter distances, each pair comprising the distance indication between said second four-dimensional vector and a particular one of said second collection of four-dimensional sets of points and the distance indication between said second four-dimensional vector and a set of four-dimensional points which is a hundred-eighty degree rotation of said particular one of said second collection of four-dimensional sets of points; (d) for each said collection of sixteen four-coordinate representational vectors, finding four representational four-coordinate vectors comprised of a combination of first and second two-dimensional coordinates from said first group of shorter distance indications, and third and fourth two-dimensional coordinates from said second group of shorter distance indications; and (e) for each said collection of sixteen four coordinate representational vectors, comparing among four distance indications from said received vector to the eight-dimensional set of subconstellation points represented by each of said four found four-coordinate representational vectors, to determine a shortest distance indication between said received vector and each subconstellation.