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Geometrically uniform codes. (English) Zbl 0734.94026
Summary: A signal space code is defined as geometrically uniform if, for any two code sequences in , there exists an isometry that maps one sequence into the other while leaving the code invariant (i.e., the symmetry group of acts transistively). Geometrical uniformity is a strong kind of symmetry that implies such properties as a) the distance profiles from code sequences in to all other code sequences are all the same, and b) all Voroni regions of code sequences in 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 Z N /Λ/Λ ' /4Z N is a lattice partition chain, and b) PSK-type trellis codes based on up to four-way partitions of a 2 n -PSK signal set.

MSC:
94B60Other types of codes
94B12Combined modulation schemes