Reduced Complexity Bounded-distance Decoding of the Leech Lattice
Ofer Amrani, Yair Be'ery, Alexander Vardy · 2005
A new efficient algorithm for bounded-distance decoding of the Leech lattice is presented. The algorithm decodes correctly at least up to the guaranteed error-correction radius of the Leech lattice. The proposed decoder is based on projecting the points of the Leech lattice onto the codewords of the (6, 3, 4) quarternary code, the hexacode H/sub 6/. Projection on the hexacode induces partition of the Leech lattice into four cosets of Q/sub 24/, beyond the conventional partition into two H/sub 24/ cosets. This enables bounded-distance decoding of the Leech lattice with only 1127 real operations in the worst case, as compared to about 3600 operations for the maximum-likelihood decoding of [9]. The proposed algorithm is at least 30% more efficient than Forney's algorithm [5] in terms of computational complexity, while the coding gain loss is no more than 0.05 dB (over BER ranging from 10/sup -1/ to 10/sup -6/ ).