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Closest point search in lattices
Open accessAbstract
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 /spl isin/ /spl Ropf//sup m/ and a generator matrix for a lattice /spl Lambda/, the algorithm computes the point of /spl Lambda/ 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.
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Metadata
- Authors
- Agrell, E., Eriksson, T., Vardy, A., & Zeger, K.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2002-08
- Volume
- 48
- Issue
- 8
- Pages
- 2201-2214
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2140940105
- Cited by
- 1,412
- References
- 0
- FWCI
- 145.61
- Type
- journal article
- Language
- en
- Open access
- green
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