Fixed Complexity LLL Algorithm

A common technique to perform lattice basis reduction is the Lenstra, Lenstra, Lovasz (LLL) algorithm. An implementation of this algorithm in real-time systems suffers from the problem of variable run-time and complexity. This correspondence proposes a modification of the LLL algorithm. The signal flow is altered to follow a deterministic structure, which promises to obtain an easier implementation as well as a fixed execution time known in advance. In the case of a maximum number of iterations as it is likely in real-time systems, our modification clearly outperforms the original LLL algorithm as far as the quality of the reduced lattice basis is concerned.

[1]  Claus-Peter Schnorr,et al.  Progress on LLL and Lattice Reduction , 2010, The LLL Algorithm.

[2]  Hendrik W. Lenstra,et al.  Integer Programming with a Fixed Number of Variables , 1983, Math. Oper. Res..

[3]  Gerald Matz,et al.  Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[4]  Wai Ho Mow,et al.  Complex Lattice Reduction Algorithm for Low-Complexity MIMO Detection , 2006, ArXiv.

[5]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[6]  Gilles Villard,et al.  Parallel lattice basis reduction , 1992, ISSAC '92.

[7]  Shafi Goldwasser,et al.  Complexity of lattice problems , 2002 .

[8]  Dirk Wübben,et al.  Near-maximum-likelihood detection of MIMO systems using MMSE-based lattice reduction , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[9]  Cong Ling,et al.  Effective LLL Reduction for Lattice Decoding , 2007, 2007 IEEE International Symposium on Information Theory.

[10]  Magnus Sandell,et al.  Complexity Study of Lattice Reduction for MIMO Detection , 2007, 2007 IEEE Wireless Communications and Networking Conference.

[11]  Wai Ho Mow,et al.  Universal lattice decoding: principle and recent advances , 2003, Wirel. Commun. Mob. Comput..

[12]  Xiaoli Ma,et al.  VLSI Implementation of a Lattice Reduction Algorithm for Low-Complexity Equalization , 2008, 2008 4th IEEE International Conference on Circuits and Systems for Communications.

[13]  Robert F. H. Fischer,et al.  Lattice-reduction-aided broadcast precoding , 2004, IEEE Transactions on Communications.