Abstract
A signal space code C is defined as geometrically uniform if, for any two code sequences in C, there exists an isometry that maps one sequence into the other while leaving the code C invariant. Geometrical uniformity, a strong kind of symmetry, implies such properties as a) the distance profiles from code sequences in C to all other code sequences are all the same, and b) all Voronoi regions of code sequences in C 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/sup N// Lambda / Lambda '/4Z/sup N/ is a lattice partition chain, and (b) phase-shift-keying (PSK)-type trellis codes based on up to four-way partitions of a 2/sup n/-PSK signal set.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Keywords
CombinatoricsMathematicsLambdaCosetGroup codeLattice (music)Discrete mathematicsBinary Golay codeIsometry (Riemannian geometry)Partition (number theory)Linear codeBlock codeAlgorithmDecoding methodsPhysicsPure mathematics
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Publication Info
- Year
- 1991
- Type
- article
- Volume
- 37
- Issue
- 5
- Pages
- 1241-1260
- Citations
- 450
- Access
- Closed
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Cite This
G. David Forney
(1991).
Geometrically uniform codes.
IEEE Transactions on Information Theory
, 37
(5)
, 1241-1260.
https://doi.org/10.1109/18.133243
Identifiers
- DOI
- 10.1109/18.133243