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.