.png){kind=icon}
返回
N-Dimensional LLL Reduction Algorithm with Pivoted Reflection
.png){kind=icon}
OA
AI
DOI：10.3390/s18010283.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
The Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm and many of its variants have been widely used by cryptography, multiple-input-multiple-output (MIMO) communication systems and carrier phase positioning in global navigation satellite system (GNSS) to solve the integer least squares (ILS) problem. In this paper, we propose an n-dimensional LLL reduction algorithm (n-LLL), expanding the Lovasz condition in LLL algorithm to n-dimensional space in order to obtain a further reduced basis. We also introduce pivoted Householder reflection into the algorithm to optimize the reduction time. For an m-order positive definite matrix, analysis shows that the n-LLL reduction algorithm will converge within finite steps and always produce better results than the original LLL reduction algorithm with n > 2. The simulations clearly prove that n-LLL is better than the original LLL in reducing the condition number of an ill-conditioned input matrix with 39% improvement on average for typical cases, which can significantly reduce the searching space for solving ILS problem. The simulation results also show that the pivoted reflection has significantly declined the number of swaps in the algorithm by 57%, making n-LLL a more practical reduction algorithm.
Keyword:
LLL reduction
pivoted reflection
integer least squares (ILS)
global navigation satellite system (GNSS)
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
3.5
论文数:
7.2W
被引数:
20.9W
机构
引用论文
Entropy Generation Methodology for Defect Analysis of Electronic and Mechanical Components—A Review.png)
EntropyOAAI
EntropyIF0
OAAI分享收藏
分享收藏Heart rate variability as a prognostic tool in cardiology. A contribution to the problem from a theoretical point of view.CirculationOAAI
CirculationIF0
OAAI分享收藏6 The actions of thyroid hormones mediated via the cell nucleus and their clinical significance
PREAI
分享收藏
查看更多内容