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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.19 No.2
- 발행연도
- 2015.6
- 수록면
- 171 - 188 (18page)
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초록· 키워드
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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´asz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.
목차
ABSTRACT
1. INTRODUCTION
2. LATTICE REDUCTION: LLL ALGORITHM
3. LLL COLUMN-WISE UPDATING AND DOWNDATING
4. LLL ROW-WISE UPDATING AND DOWNDATING
5. ROUNDING ERROR ANALYSIS
6. NUMERICAL RESULTS
7. CONCLUDING REMARKS
REFERENCES
참고문헌 (20)
참고문헌 신청
[학술지(정기간행물)] - A. K. Lenstra / 1982 / Factoring polynomials with rational coefficients / Mathematische Annalen 261 (4) : 515 ~ 534
[학술대회논문] - P. Nguyen / 1838 / Lattice reduction in cryptology: An update, in Algorithmic number theory: 4th international symposium - ANTS-IV / Lecture Notes in Computer Sciences 1838 : 85 ~ 112
[학술지(정기간행물)] - C. P. Schnorr / 1987 / A hierarchy of polynomial time lattice basis reduction algorithms / Theoretical Computer Science 53 : 201 ~ 224
[학술지(정기간행물)] - K. Lee / 2007 / Optimal lattice-reduction aided successive interference cancellation for mimo systems / IEEE transaction on Wireless Communications 6 (7) : 2438 ~ 2443
[학술대회논문] - C. Windpassinger / 2003 / Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction / Proc. IEEE Information Theory Workshop : 345 ~ 348
[학술대회논문] - P. Nguyen / 1838 / Lattice reduction in cryptology: An update, in Algorithmic number theory: 4th international symposium - ANTS-IV / Lecture Notes in Computer Sciences 1838 : 85 ~ 112
[학술지(정기간행물)] - C. P. Schnorr / 1987 / A hierarchy of polynomial time lattice basis reduction algorithms / Theoretical Computer Science 53 : 201 ~ 224
[학술지(정기간행물)] - K. Lee / 2007 / Optimal lattice-reduction aided successive interference cancellation for mimo systems / IEEE transaction on Wireless Communications 6 (7) : 2438 ~ 2443
[학술대회논문] - C. Windpassinger / 2003 / Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction / Proc. IEEE Information Theory Workshop : 345 ~ 348
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