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

This paper considers two kinds of algorithms. (i) If # is a binary code of length n, a ‘‘soft decision’’ decoding algorithm for # changes an arbitrary point of Rn into a nearest codeword (nearest in Euclidean distance). (ii) Similarly a decoding algorithm for a lattice Λ in Rn changes an arbitrary point of Rn into a closest lattice point. Some general methods are given for constructing such algorithms, and are used to obtain new and faster decoding algorithms for the Gosset lattice E 8 , the Golay code and the Leech lattice. _ ______________ * This paper appeared in ‘‘IEEE Trans. Information Theory’’, vol. 32 (1986), 41–50.