Some Properties of Successive Minima and Their Applications

A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical applications points of view. In this paper, we first study some properties of successive minima and then employ some of them to improve the suboptimal algorithm for solving an optimization problem about maximizing the achievable rate of the integer-forcing strategy for cloud radio access networks in [1].