Reduced Complexity Bounded .Distance Decoding of the Leech Lattice

A bstmct-A new efficient algorithm for bounded-distance decoding of the Leech la t t ice is presented. The algori thm decodes correctly at least ulp 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) quar te rnary code, the hezacode Ne. Project ion on the hexacode induces par t i t ion of the Leech lattice into four cosets of Q24, beyond t h e conventional partition into two H24 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 t h e maximum-likelihood decoding of [9]. The proposed algori thm is a t least 30% more efficient than Forney’s a lgori thm [5] in te rms of computational complexity, while t h e coding gain loss is no more than 0.05 dB (over BER ranging from IO-’ to ).