1. Apparatus for transmitting a stream of information bits by sending corresponding signals over a channel in a plurality of signaling slots, comprising means for encoding the information bits that appear during a block of at least two said signaling slots by adding at least one redundant bit, to form a set of signal point selection bits for said block, means for selecting, for each said set of signal point selection bits a multi-dimensional signal point drawn from a multi-dimensional constellation for said block, said multi-dimensional signal point selected for a particular said block being dependent on the multi-dimensional signal point selected for at least one other said block, said means for selecting being connected to be responsive to said means for encoding, wherein said means for selecting establishes a correspondence between each possible combination of said signal point selection bits and the coordinates of a multi-dimensional signal point in said multi-dimensional constellation, wherein said means for encoding and said means for selecting define a partitioning of said multi-dimensional constellation into a plurality of multi-dimensional subsets and determine the subset from which said multi-dimensional signal point is selected based upon at least one of said signal point selection bits, said multi-dimensional constellation being a concatenation of constituent constellations each of which has fewer dimensions than said multi-dimensional constellation and is partitioned into constituent subsets, each said multi-dimensional subset being based upon said constituent subsets but being other than a concatenation of constituent subsets of said constituent constellations, and means for modulating at least one carrier for transmission over said channel in accordance with each selected said multi-dimensional signal point, said means for modulating being connected to be responsive to said means for selecting, and wherein said constituent subsets in each said constituent constellation are grouped to form constituent families such that the minimum distance between constituent points within each said constituent subset is greater than the minimum distance between constituent points within each said constituent family, which is in turn greater than the minimum distance between constituent points within said constituent constellation, said multi-dimensional constellation is partitioned into said multi-dimensional subsets based on said distances of said constituent families and subsets, said multi-dimensional subsets are grouped to form multi-dimensional families also based on said distances, and said constituent family comprises constituent subfamilies each of which comprises a plurality of said constituent subsets chosen such that the minimum distance between constituent points within each said constituent subfamily is greater than the minimum distance between constituent points within each said constituent family and is less than the minimum distance between constituent points within each said constituent subset, and said multi-dimensional constellation is partitioned into said multi-dimensional subsets also based on said distances of said constituent subfamilies.