A Jacobi Method for Lattice Basis Reduction

Abstract

Abstract-Lattice reduction aided decoding has been successfully used in wireless communications. In this paper, we propose a Jacobi method for lattice basis reduction. Jacobi method is attractive, because it is inherently parallel. Thus high performance can be achieved by exploiting multiprocessor and/or multicore architectures. We also present our experimental results on the convergence of our method and the comparison with the LLL algorithm, a lattice basis reduction method widely used in wireless communication applications.

A Hybrid Method for Lattice-Reduction-Aided MIMO Detection

“…. Thus, we have π/3 ≤ θ ≤ 2π/3 [16]. We generalize the definition of the Lagrange reduction to n-dimensional lattices.…”

An enhanced Jacobi method for lattice-reduction-aided MIMO detection

“…The Lagrange iteration is a part of our EJacobi method presented in the section 3.3. We also recall the Jacobi method [13,15] in this section.…”

“…S. Qiao introduced a Jacobi method for lattice basis reduction in 2012 [13], which embeds the Lagrange algorithm to reduce every pair of basis vectors in an n dimensional lattice and produces a reduced basis defined below.…”

“…Given the Gram matrix G and i < j, Procedure LAGRANGEIT(G, i, j) produces a unimodular matrix Z [13] so that AZ performs one iteration of the Lagrange algorithm on a i and a j , where a i is updated by a i ← a i − qa j and the length a i 2 is reduced, hence a i and a j get closer to being orthogonal to each other.…”

“…In this paper, we present an enhanced Jacobi method, the EJacobi method, for lattice basis reduction based on the Jacobi method [13] introduced by S. Qiao. Our experimental results indicate that the EJacobi method performs better than the LLL algorithm in both output quality and time consumption.…”