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Maximum likelihood decoding of the Leech lattice

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2 Author(s)
Vardy, A. ; IBM Almaden Res. Center, San Jose, CA, USA ; Be'ery, Y.

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

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Information Theory, IEEE Transactions on  (Volume:39 ,  Issue: 4 )