The Diagonal Reduction Algorithm Using Fast Givens

Recently, a new lattice basis reduction notion, called diagonal reduction, was proposed for lattice-reduction-aided detection (LRAD) of multiinput multioutput (MIMO) systems. In this paper, we improve the efficiency of the diagonal reduction algorithm by using the fast Givens transformations. The technique of the fast Givens is applicable to a family of LLL-type lattice reduction methods to improve efficiency. Also, in this paper, we investigate dual diagonal reduction and derive an upper bound of the proximity factors for a family of dual reduction aided successive interference cancelation (SIC) decoding. Our upper bound not only extends an existing bound for dual LLL reduction to a family of dual reduction methods, but also improves the existing bound.

[1]  Jacques Stern,et al.  The hardness of approximate optima in lattices, codes, and systems of linear equations , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[2]  Alexander Vardy,et al.  Closest point search in lattices , 2002, IEEE Trans. Inf. Theory.

[3]  Phong Q. Nguyen,et al.  The LLL Algorithm - Survey and Applications , 2009, Information Security and Cryptography.

[4]  Wai Ho Mow,et al.  Dual-Lattice Ordering and Partial Lattice Reduction for SIC-Based MIMO Detection , 2009, IEEE Journal of Selected Topics in Signal Processing.

[5]  Cong Ling.  Towards Characterizing the Performance of Approximate Lattice Decoding in MIMO Communications , 2011 .

[6]  Gene H. Golub,et al.  Matrix computations , 1983 .

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

[8]  Claus-Peter Schnorr,et al.  Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems , 1991, FCT.

[9]  Wen Zhang,et al.  A Diagonal Lattice Reduction Algorithm for MIMO Detection , 2012, IEEE Signal Processing Letters.

[10]  Björn E. Ottersten,et al.  On the complexity of sphere decoding in digital communications , 2005, IEEE Transactions on Signal Processing.

[11]  Babak Hassibi,et al.  On the sphere-decoding algorithm I. Expected complexity , 2005, IEEE Transactions on Signal Processing.

[12]  László Babai,et al.  On Lovász’ lattice reduction and the nearest lattice point problem , 1986, Comb..

[13]  Cong Ling,et al.  On the Proximity Factors of Lattice Reduction-Aided Decoding , 2010, IEEE Transactions on Signal Processing.

[14]  Xiao-Wen Chang,et al.  Partial LLL Reduction , 2012, ArXiv.

[15]  Amir K. Khandani,et al.  LLL Reduction Achieves the Receive Diversity in MIMO Decoding , 2006, IEEE Transactions on Information Theory.

[16]  Wen Zhang,et al.  HKZ and Minkowski Reduction Algorithms for Lattice-Reduction-Aided MIMO Detection , 2012, IEEE Transactions on Signal Processing.

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

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