A general combinatorial sphere decoder and its application

Abstract

The conventional problem of searching the shortest vector z of a N-dimensional lattice L(H) with generating matrix HisinRNtimesM is considered in a more general setting. There are P generating matrices HiisinRNtimesM(i=1,2,...,P) of the P lattices L(Hi). For a (bounded) integer vector bisinZM , we obtain P lattice points Hib. Let di be the Euclidean norm of Hib. The problem of interest is how to search for a vector b so that the maximum of di 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