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AN ENHANCED JACOBI METHOD FOR LATTICEREDUCTIONAIDED MIMO DETECTION
"... Lattice reduction aided decoding has been successfully used for signal detection in multiinput and multioutput (MIMO) systems and many other wireless communication applications. In this paper, we propose a novel enhanced Jacobi (short as EJacobi) method for lattice basis reduction. To assess the per ..."
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Lattice reduction aided decoding has been successfully used for signal detection in multiinput and multioutput (MIMO) systems and many other wireless communication applications. In this paper, we propose a novel enhanced Jacobi (short as EJacobi) method for lattice basis reduction. To assess the performance of the new EJacobi method, we compared it with the LLL algorithm, a widely used algorithm in wireless communications. Our experimental results show that the EJacobi method is more efficient and produces better results measured by both orthogonality defect and condition number than the LLL algorithm.
A GPU Implementation of a Jacobi Method for Lattice Basis Reduction
, 2013
"... This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is about twice as fast as the wellknown LLL lattice reduction ..."
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This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is about twice as fast as the wellknown LLL lattice reduction algorithm.
General Terms Algorithms and Theory
"... The famous LLL algorithm is the first polynomial time lattice reduction algorithm which is widely used in many applications. In this paper, we prove the convergence of a novel polynomial time lattice reduction algorithm, called the Jacobi method introduced by S. Qiao [23], and show that it has the s ..."
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The famous LLL algorithm is the first polynomial time lattice reduction algorithm which is widely used in many applications. In this paper, we prove the convergence of a novel polynomial time lattice reduction algorithm, called the Jacobi method introduced by S. Qiao [23], and show that it has the same complexity as the LLL algorithm. Our experimental results show that the Jacobi method outperforms the LLL algorithm in not only efficiency, but also orthogonality defect of the bases it produces.
A Hybrid Method for Lattice Basis Reduction
, 2014
"... Lattice reduction has a wide range of applications. In this paper, we first present a polynomial time Jacobi method for lattice basis reduction bymodifying the condition for the Lagrange reduction and integrating the size reduction into the algorithm. We show that the complexity of the modified Jaco ..."
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Lattice reduction has a wide range of applications. In this paper, we first present a polynomial time Jacobi method for lattice basis reduction bymodifying the condition for the Lagrange reduction and integrating the size reduction into the algorithm. We show that the complexity of the modified Jacobi algorithm isO(n5 logB), where n is the dimension of the lattice and B is the maximum length of the input lattice basis vectors. To improve the quality of the computed bases, we then enhance our method by including a postprocessing without compromising the complexity. Our experiments show that our hybrid algorithm computes better reduced bases than the wellknown LLL algorithm in terms of both the orthogonality defect and the condition number of the basis matrix. Moreover, although our algorithm has higher complexity than the LLL algorithm, it runs faster for problems of sizes under 90.
A Polynomial Time Jacobi Method for Lattice Basis Reduction
, 2012
"... Among all lattice reduction algorithms, the LLL algorithm is the first and perhaps the most famous polynomial time algorithm, and it is widely used in many applications. In 2012, S. Qiao [24] introduced another algorithm, the Jacobi method, for lattice basis reduction. S. Qiao and Z. Tian [25] impro ..."
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Among all lattice reduction algorithms, the LLL algorithm is the first and perhaps the most famous polynomial time algorithm, and it is widely used in many applications. In 2012, S. Qiao [24] introduced another algorithm, the Jacobi method, for lattice basis reduction. S. Qiao and Z. Tian [25] improved the Jacobi method further to be polynomial time but only produces a QuasiReduced basis. In this paper, we present a polynomial time Jacobi method for lattice basis reduction (short as PolyJacobi method) that can produce a reduced basis. Our experimental results indicate that the bases produced by PolyJacobi method have almost equally good orthogonality defect as the bases produced by the Jacobi method.
A PARALLEL JACOBITYPE LATTICE BASIS REDUCTION ALGORITHM
"... Abstract. This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is twice as fast as the wellknown LLL lattice reduct ..."
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Abstract. This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is twice as fast as the wellknown LLL lattice reduction algorithm. Key words. Lattice basis reduction, Jacobi method, GPU. 1.