Geometrically uniform partitions of L*MPSK constellations and related binary trellis codes

S. Benedetto, R. Garello, M. Mondin, G. Montorsi
1993 IEEE Transactions on Information Theory  
The recently developed theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK constellations. The symmetry group of an L X MPSK constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L X MPSK ( M = 4,8,16 and L = 1 , 2 , 3 , 4 ) constellations are found, which present good characteristics in terms
more » ... cteristics in terms of the set of distances at a given partition level, the maximum obtainable rotational invariance, and the isomorphism of the quotient group associated with the partition. These partitions are used as starting points in a search for good geometrically uniform trellis codes based on binary convolutional codes. Index Terms-Trellis-coded modulation (TCM), multidimensional (multi-D) signal sets, phase-shift keying (PSK), geometrically uniform codes.
doi:10.1109/18.265490 fatcat:zc3qp2g6wja63bjpv2w3zojim4