- Volume 19 Issue 2
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EFFICIENT LATTICE REDUCTION UPDATING AND DOWNDATING METHODS AND ANALYSIS
- PARK, JAEHYUN (DEPARTMENT OF ELECTRONIC ENGINEERING, PUKYONG NATIONAL UNIVERSITY) ;
- PARK, YUNJU (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, KOREA SCIENCE ACADEMY OF KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY)
- Received : 2015.02.12
- Accepted : 2015.05.06
- Published : 2015.06.25
In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov
Supported by : Pukyong National University
- A. K. Lenstra, J. H. W. Lenstra, and L. Lovasz, "Factoring polynomials with rational coefficients," Mathematische Annalen, vol. 261, no. 4, pp. 515-534, Dec. 1982. https://doi.org/10.1007/BF01457454
- P. Nguyen and J. Stern, "Lattice reduction in cryptology: An update," in Algorithmic number theory: 4th international symposium - ANTS-IV, Lecture Notes in Computer Sciences, vol. 1838. Springer, 2000, pp. 85-112.
- C. P. Schnorr, "A hierarchy of polynomial time lattice basis reduction algorithms," Theoretical Computer Science, vol. 53, pp. 201-224, 1987. https://doi.org/10.1016/0304-3975(87)90064-8
- K. Lee, J. Chun, and L. Hanzo, "Optimal lattice-reduction aided successive interference cancellation for mimo systems," IEEE transaction on Wireless Communications, vol. 6, no. 7, pp. 2438-2443, July 2007. https://doi.org/10.1109/TWC.2007.06058
- C. Windpassinger and R. F. H. Fischer, "Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction," in Proc. IEEE Information Theory Workshop (ITW), Mar. 2003, pp. 345-348.
- H. Yao and G. W. Wornell, "Lattice-reduction-aided detectors for MIMO communication systems," in Proc. IEEE Global Telecommunication Conference, Taipei, Taiwan, vol. 1, Nov. 2002, pp. 424-428.
- D. Wubben, R. Bohnke, V. Kuhn, and K. D. Kammeyer, "Near-maximum-likelihood detection of MIMO systems using MMSE-based lattice-reduction," in Proc. IEEE International Conference on Communications, vol. 2, June 2004, pp. 798-802.
- J. Park and J. Chun, "Improved lattice reduction-aided MIMO successive interference cancellation under channel estimation errors," IEEE Trans. Signal Processing, vol. 60, no. 6, pp. 3346-3351, June 2012. https://doi.org/10.1109/TSP.2012.2189107
- J. Park and J. Chun, "Efficient lattice-reduction-aided successive interference cancellation for clustered multiuser MIMO system," IEEE transactions on Vehicular Technology, vol. 61, no. 8, pp. 3643-3655, Oct. 2012. https://doi.org/10.1109/TVT.2012.2201967
- A. Storjohann, "Faster algorithms for integer lattice basis reduction," Swiss Federal Institute of Technology, Departement Informatik, ETH Zurich, Tech. Rep. TR 249, July 1996.
- H. Koy and C. P. Schnorr, "Segment LLL-reduction of lattice bases," in in: Cryptograhpy and Lattices, Lecture Notes in Computer Sciences, vol. 2146. New York: Springer, 2001, pp. 67-80.
- H. Koy and C. P. Schnorr, "Segment LLL-reduction with floating point orthogonalization," in in: Cryptograhpy and Lattices, Lecture Notes in Computer Sciences, vol. 2146. Springer, 2001, pp. 81-96.
- N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed. Philadelphia: SIAM, 2002.
- J. H. Wilkinson, The Algebraic Eigenvalue Problem. Clarendon Press, Oxford, 1965.
- C. C. Paige, "Error analysis of some techniques for updating orthogonal decompositions," Mathematics of Computation, vol. 34, no. 150, pp. 465-471, 1980. https://doi.org/10.1090/S0025-5718-1980-0559196-9
- G. Hargreaves, "Topics in matrix computations: Stability and efficiency of algorithms," Ph.D. dissertation, Univ. of Manchester, Manchester, UK, 2005.
- A. Bojanczyk, N. J. Higham, and H. Patel, "Solving the indefinite least squares problem by hyperbolic QR factorization," SIAM Journal on Matrix Analysis and Applications, vol. 24, no. 4, pp. 914-931, 2003. https://doi.org/10.1137/S0895479802401497
- M. C. Cary, "Lattice basis reduction: Algorithms and applications," Unpublished draft available at http://www.cs.washington.edu/homes/cary/lattice.pdf, Feb. 2002.
- G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. Baltimore: Johns Hopkins Univ. Press, 1996.
- G. W. Stewart, "The effects of rounding error on an algorithm for downdating a cholesky factorization," Journal of the Institute of Mathematics and its Applications, vol. 23, no. 2, pp. 203-213, 1979. https://doi.org/10.1093/imamat/23.2.203