A general combinatorial sphere decoder and its application

The conventional problem of searching the shortest vector z of a N-dimensional lattice L(H) with generating matrix HisinR^NtimesM is considered in a more general setting. There are P generating matrices H_iisinR^NtimesM(i=1,2,...,P) of the P lattices L(H_i). For a (bounded) integer vector bisinZ^M , we obtain P lattice points H_ib. Let d_i be the Euclidean norm of H_ib. The problem of interest is how to search for a vector b so that the maximum of d_i is minimized. We propose a new sphere decoder called combinatorial sphere decoder (CSD) to solve this problem. One of the applications of the new CSD is presented in detail to show its effectiveness