Geometrically uniform partitions of L*MPSK constellations and related binary trellis codes
Open Access
- 1 January 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 39 (6) , 1773-1798
- https://doi.org/10.1109/18.265490
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 codesKeywords
This publication has 11 references indexed in Scilit:
- Convolutional codes over groupsIEEE Transactions on Information Theory, 1996
- The dynamics of group codes: state spaces, trellis diagrams, and canonical encodersIEEE Transactions on Information Theory, 1993
- Geometrically uniform codesIEEE Transactions on Information Theory, 1991
- Fundamental Algorithms for Permutation GroupsPublished by Springer Nature ,1991
- Trellis-coded multidimensional phase modulationIEEE Transactions on Information Theory, 1990
- Multilevel codes based on partitioningIEEE Transactions on Information Theory, 1989
- Groups and SymmetryPublished by Springer Nature ,1988
- Channel coding with multilevel/phase signalsIEEE Transactions on Information Theory, 1982
- On the existence of group codes for the Gaussian channelIEEE Transactions on Information Theory, 1972
- Group codes for the Gaussian channel (Abstr.)IEEE Transactions on Information Theory, 1968