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

Author

Benedetto, Sergio ; Garello, Roberto ; Mondin, Marina ; Montorsi, Guido

Author_Institution

Dipartimento di Elettronica, Politecnico di Torino, Italy

Volume

39

Issue

6

fYear

1993

fDate

11/1/1993 12:00:00 AM

Firstpage

1773

Lastpage

1798

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

Keywords

convolutional codes; phase shift keying; trellis codes; M-ary PSK; MPSK; PSK constellations; algorithms; binary convolutional codes; binary trellis codes; distances; geometrically uniform partitions; geometrically uniform trellis codes; isomorphism; multidimensional PSK; phase shift keying; quotient group; rotational invariance; signal constellation; symmetry group; Constellation diagram; Convolutional codes; Digital communication; Digital modulation; Labeling; Modulation coding; Multidimensional systems; Partitioning algorithms; Phase modulation; Phase shift keying;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.265490

Filename

265490