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Closest point search in lattices

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4 Author(s)
E. Agrell ; Dept. of Signals & Syst., Chalmers Univ. of Technol., Goteborg, Sweden ; T. Eriksson ; A. Vardy ; K. Zeger

In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr-Euchner (1995) variation of the Pohst (1981) method, is implemented. Given an arbitrary point x ∈ Rm and a generator matrix for a lattice Λ, the algorithm computes the point of Λ that is closest to x. The algorithm is shown to be substantially faster than other known methods, by means of a theoretical comparison with the Kannan (1983, 1987) algorithm and an experimental comparison with the Pohst (1981) algorithm and its variants, such as the Viterbo-Boutros (see ibid. vol.45, p.1639-42, 1999) decoder. Modifications of the algorithm are developed to solve a number of related search problems for lattices, such as finding a shortest vector, determining the kissing number, computing the Voronoi (1908)-relevant vectors, and finding a Korkine-Zolotareff (1873) reduced basis.

Published in:

IEEE Transactions on Information Theory  (Volume:48 ,  Issue: 8 )