A pivoted LLL algorithm

N-Dimensional LLL Reduction Algorithm with Pivoted Reflection

The Lenstra-Lenstra-Lovász (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 t...

An improved LLL algorithm

6 The LLL algorithm has received a lot of attention as an effective numerical tool for preconditioning 7 an integer least squares problem. However, the workings of the algorithm are not well understood. In this 8 paper, we present a new way to look at the LLL reduction, which leads to a new implementation method 9 that performs better than the original LLL scheme. 10 © 2007 Published by Elsevie...

Modified LLL algorithm with shifted start column

Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless communication. The complexity of the different systems models challenge different researches to get a good complexity to performance balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovàsz (LLL) algorithm bring more resources to investigate and can contribute to the complexity reduction ...

Conditioning Properties of the LLL Algorithm

Although the LLL algorithm was originally developed for lattice basis reduction, the method can also be used to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoting scheme works well in practice.

The History of the LLL-Algorithm