Efficient bounded-distance decoding of the hexacode and associated decoders for the leech lattice and the golay code

Two soft-decision decoding algorithms for the (6, 3, 4) quaternary code hexacode are presented. Both algorithms realize half the minimum Euclidean distance of the code. The proposed algorithms are most practical. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed with at most 187 and 519 real-number operations respectively. Compare this to 651, respectively 3595, operations required by the best known maximum likelihood decoders of [5], [6], and 431, respectively 1007, operations required by the bounded-distance decoders of [7]. We present some simulation results for the proposed Leech lattice decoders revealing near-optimal performance. A comparison to known trellis codes is also provided.