A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice v represented by some basis, and a target point y, nd the lattice point closest to y. Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance 1(v) of the lattice. Specically, in the -Bounded Distance Decoding problem (BDD), we are given a lattice v and a vector y (within distance