Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice

Two kinds of algorithms are considered.1)If *** is a binary code of lengthn, a "soft decision" decoding algorithm for *** changes an arbitrary point ofR^{n}into a nearest codeword (nearest in Euclidean distance).2)Similarly, a decoding algorithm for a lattice\LambdainR^{n}changes an arbitrary point ofR^{n}into a closest lattice point. Some general methods are given for constructing such algorithms, ami are used to obtain new and faster decoding algorithms for the Gosset latticeE_{8}, the Golay code the Leech lattice.