Comparative study on algorithms for solving the Integer Least Squares problem

This paper studies and compares the techniques commonly used to solve the Integer Lease Squares (ILS) problem. In general, ILS is a NP hard problem. However, by introducing some basis reduction algorithms and carefully designing the search strategy, much more efficient solving procedures (compared with blind search) can be developed. A general method is to reduce the basis first and then perform an exhaustive search within certain region. In this paper, several widely used basis reduction (or decorrelation) algorithms are presented, the Korkine-Zolotareff (KZ) reduction, LLL reduction, integer inverse Cholesky decorrelation (IICD) and integer Gaussian decorrelation (IGD). Their pros and cons are evaluated by the simulation results, which show that none of them can be uniformly superior than the others. Further, an efficient discrete search algorithm, which incorporates the Pohst strategy, Schnorr-Euchner strategy and shrinking strategy, is presented in great detail in the hope that the reader can implement it easily even without knowing the background knowledge.