The theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK (phase shift keying) constellations. The symmetry group of an L×MPSK (M-ary PSK) 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×MPSK (M=4,8,16 and L=1,2,3,4) constellations are found, which present good characteristics 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.

Geometrically uniform partitions of L×MPSK constellations and related binary trellis codes / Benedetto, Sergio; Garello, Roberto; Mondin, Marina; Montorsi, Guido. - In: IEEE TRANSACTIONS ON INFORMATION THEORY. - ISSN 0018-9448. - STAMPA. - 39:6(1993), pp. 1773-1798. [10.1109/18.265490]

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

BENEDETTO, Sergio;GARELLO, Roberto;MONDIN, Marina;MONTORSI, Guido
1993

Abstract

The theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK (phase shift keying) constellations. The symmetry group of an L×MPSK (M-ary PSK) 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×MPSK (M=4,8,16 and L=1,2,3,4) constellations are found, which present good characteristics 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/1402488
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