DECODING AFFINE REFLECTION GROUP CODES WITH TRELLISES
We present two decoding methods (called hybrid and lattice cosets) for affine reflection group codes (ARGC) of any dimension. The algorithms are based on viewing the affine reflection group as a semi-direct product of a crystallographic finite reflection group and its coroot lattice. The proposed lattice cosets method gives an explicit method for drawing a trellis diagram representation of ARGC. The complexities of these two decoding methods, as well as the trade-offs between them, are discussed.
affine reflection groups group codes lattice codes trellis decoding