Approximate Lattice Decoding: Primal Versus Dual Basis Reduction

Lattice decoding enables significant complexity reduction in multi-input multi-output (MIMO) communications. Unlike most work on the lattice-reduction-aided decoding technique, this paper is aimed at a comparative study of primal versus dual basis reduction for approximate lattice decoding. We derive the respective proximity factors for the two methods, which measure the performance gap to maximum-likelihood (ML) decoding. It is found that in many cases reducing the dual can result in smaller proximity factors than reducing the primal basis

[1]  W. Banaszczyk.  New bounds in some transference theorems in the geometry of numbers , 1993 .

[2]  Gregory W. Wornell,et al.  Lattice-reduction-aided detectors for MIMO communication systems , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[3]  Amir K. Khandani,et al.  LLLl lattice-basis reduction achieves the maximum diversity in MIMO systems , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[4]  Cong Ling.  Towards characterizing the performance of appriximate lattice decoding , 2006 .

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

[6]  R. Fischer,et al.  Optimum and Sub-Optimum Lattice-Reduction-Aided Detection and Precoding for MIMO Communications , 2022 .

[7]  C. P. Schnorr,et al.  A Hierarchy of Polynomial Time Lattice Basis Reduction Algorithms , 1987, Theor. Comput. Sci..

[8]  Jeffrey C. Lagarias,et al.  Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice , 1990, Comb..

[9]  U. Fincke,et al.  Improved methods for calculating vectors of short length in a lattice , 1985 .

[10]  F. Thorne,et al.  Geometry of Numbers , 2017, Algebraic Number Theory.

[11]  Reinaldo A. Valenzuela,et al.  V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel , 1998, 1998 URSI International Symposium on Signals, Systems, and Electronics. Conference Proceedings (Cat. No.98EX167).

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

[13]  Emanuele Viterbo,et al.  A universal lattice code decoder for fading channels , 1999, IEEE Trans. Inf. Theory.

[14]  Wai Ho Mow,et al.  Multiple-antenna differential lattice decoding , 2005, IEEE Journal on Selected Areas in Communications.

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

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

[17]  C. A. Rogers,et al.  An Introduction to the Geometry of Numbers , 1959 .