Title :
Maximum likelihood decoding of the Leech lattice
Author :
Vardy, Alexander ; Be´ery, Y.
Author_Institution :
IBM Almaden Res. Center, San Jose, CA, USA
fDate :
7/1/1993 12:00:00 AM
Abstract :
An algorithm for maximum likelihood decoding of the Leech lattice is presented. The algorithm involves projecting the points of the Leech lattice directly onto the codewords of the (6,3,4) quaternary code-the hexacode. Projection on the hexacode induces a partition of the Leech lattice into four cosets of a certain sublattice 24. Such a partition into cosets enables maximum likelihood decoding of the Leech lattice with 3595 real operations in the worst case and only 2955 operations on the average. This is about half the worst case and the average complexity of the best previously known algorithm
Keywords :
decoding; lattice theory and statistics; maximum likelihood estimation; (6,3,4) quaternary code; Leech lattice; binary Golay code; cosets; hexacode; lattice partitions; maximum likelihood decoding; AWGN channels; Arithmetic; Computational geometry; Constellation diagram; Gain; Lattices; Maximum likelihood decoding; Out of order; Partitioning algorithms; Random access memory;
Journal_Title :
Information Theory, IEEE Transactions on
