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Zbl 0734.94026
Forney, G.David jun.
Geometrically uniform codes. (English)
[J] IEEE Trans. Inf. Theory 37, No.5, 1241-1260 (1991). ISSN 0018-9448

Summary: A signal space code ${\bbfC}$ is defined as geometrically uniform if, for any two code sequences in ${\bbfC}$, there exists an isometry that maps one sequence into the other while leaving the code ${\bbfC}$ invariant (i.e., the symmetry group of ${\bbfC}$ acts transistively). Geometrical uniformity is a strong kind of symmetry that implies such properties as a) the distance profiles from code sequences in ${\bbfC}$ to all other code sequences are all the same, and b) all Voroni regions of code sequences in ${\bbfC}$ have the same shape. It is stronger than Ungerboeck-Zehavi-Wolf symmetry or Calderbank-Sloane regularity. Nonetheless, most known good classes of signal space codes are shown to be generalized coset codes, and therefore geometrically uniform, including a) lattice-type trellis codes based on lattice partitions $\Lambda/\Lambda'$ such that $Z\sp N/\Lambda/\Lambda'/4Z\sp N$ is a lattice partition chain, and b) PSK-type trellis codes based on up to four-way partitions of a $2\sp n$-PSK signal set.

MSC 2000:: *94B60 Other types of codes
94B12 Combined modulation schemes

Keywords: group codes; geometric codes; Euclidean-space codes; signal space code; Geometrical uniformity; distance profiles; Voroni regions of code sequences; Ungerboeck-Zehavi-Wolf symmetry; Calderbank-Sloane regularity; lattice-type trellis codes; PSK-type trellis codes

Cited in: Zbl 1231.94070 Zbl 0838.94015 Zbl 0804.94004

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