Geometrically uniform codes

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 Z^N/Λ/Λ´/4Z^N 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 set