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 length n , a "soft decision" decoding algorithm for *** changes an arbitrary point of R^{n} into a nearest codeword (nearest in Euclidean distance). 2) Similarly, a decoding algorithm for a lattice \Lambda in R^{n} changes an arbitrary point of R^{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 lattice E_{8} , the Golay code the Leech lattice.

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