| 摘要 |
A method is disclosed for determining with only sixty-four distance comparisons the distances between a received eight-dimensional vector comprised of four twodimensional coordinates and each of sixteen non-overlapping subconstellations. In order to limit the comparisons, each subconstellation is represented by a collection of sixteen representational four-coordinate vectors, with each collection having four groups of vectors of the form (a, b, c, d ) (a+2, b+2, c, d ) (a, b, c+2, d+2) (a+2, b+2, c+2, d+2) where each letter represents in a different plane one of a set of points T(O) and its ninety, one hundred and eighty, and two hundred and seventy degree rotations, and +2 represents a one hundred and eighty degree rotation. Knowing the distance between each coordinate of the received vector and each set of points, if the received vector is broken into two two-coordinate vectors, eight comparisons may be made to find the eight shortest combinations of the two-coordinate representative vectors for the first two planes, and eight additional comparisons for the second two planes. By combining the two groups of two-coordinate shorter vectors, sixty-four combinations are found for the sixteen collections of four-coordinate representational vectors; four for each collection. Three comparisons for each group may then be made for each subconsteliation to find the representational vector representing the fourcoordinate (eight-dimensional) point closest to the received vector.
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