Efficient bounded-distance decoding of the hexacode and associated decoders for the Leech lattice and the Golay code

摘要

Two soft-decision algorithms for decoding the (6,3,4) quaternary code, the hexacode, are presented. Both algorithms have the same guaranteed error correction radius as that of maximum-likelihood decoding. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed in at most 187 and 519 real operations respectively. We present some simulation results for the Leech lattice decoder revealing near-optimal performance. A comparison to known trellis codes is also provided.