Geometrically uniform codes
- 1 January 1991
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 37 (5) , 1241-1260
- https://doi.org/10.1109/18.133243
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 Λ/Λ' such that ZN/Λ/Λ'/4ZN is a lattice partition chain, and (b) phase-shift-keying (PSK)-type trellis codes based on up to four-way partitions of a 2n-PSK signal setKeywords
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