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 (i.e., the symmetry group of C acts transistively). Geometrical uniformity is a strong kind of symmetry that 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(N)/LAMBDA/LAMBDA'/4Z(N) is a lattice partition chain, and b) PSK-type trellis codes based on up to four-way partitions of a 2n-PSK signal set.