{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T03:11:27Z","timestamp":1787713887614,"version":"build-2784847793"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>Most of the existing methods that are used to solve the closest lattice point problem are based on an efficient search of the lattice points. In this paper a novel alternative approach is suggested where the closest point to a given vector is found by calculating which Voronoi cell contains this vector in an iterative manner. Each iteration is made of simple \u201cslicing\u201d operations, using a list of the Voronoi relevant vectors that define the basic Voronoi cell of the lattice. The algorithm is guaranteed to converge to the closest lattice point in a finite number of steps. The method is suitable, for example, for decoding of multi-input multi-output (MIMO) communication problems. The average computational complexity of the proposed method is comparable to that of the efficient variants of the sphere decoder, but its computational variability is smaller.<\/jats:p>","DOI":"10.1137\/060676362","type":"journal-article","created":{"date-parts":[[2009,4,9]],"date-time":"2009-04-09T18:01:46Z","timestamp":1239300106000},"page":"715-731","source":"Crossref","is-referenced-by-count":23,"title":["Finding the Closest Lattice Point by Iterative Slicing"],"prefix":"10.1137","volume":"23","author":[{"given":"Naftali","family":"Sommer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meir","family":"Feder","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ofir","family":"Shalvi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,4,9]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.800499"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.917684"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"O. Shalvi, N. Sommer, and M. Feder,\n                      Signal Codes\n                      , in Proceedings of the IEEE Information Theory Workshop, Paris, 2003, pp. 332\u2013336.","DOI":"10.1109\/ITW.2003.1216761"},{"key":"R4","unstructured":"P. van Emde Boas,\n                      Another NP-complete Partition Problem and the Complexity of Computing Short Vectors in a Lattice\n                      , Report 81-04, Mathematisch Instituut, Amsterdam, The Netherlands, 1981."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/18.915688"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1985-0777278-8"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581144"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"N. Sommer, M. Feder, and O. Shalvi,\n                      Closest point search in lattices using sequential decoding\n                      , in Proceedings of the IEEE International Symposium on Information Theory (ISIT), Adelaide, Australia, 2005, pp. 1053\u20131057.","DOI":"10.1109\/ISIT.2005.1523500"},{"key":"R9","unstructured":"R. Gowaikar and B. Hassibi,\n                      Efficient maximum-likelihood decoding via statistical pruning\n                      , IEEE Trans. Inform. Theory, submitted."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.817444"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"J. H. Conway and N. J. A. Sloane,\n                      Sphere Packings, Lattices and Groups\n                      , 3rd ed., Springer-Verlag, New York, 1999.","DOI":"10.1007\/978-1-4757-6568-7"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2005.850352"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060676362","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:34:37Z","timestamp":1787322877000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060676362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/060676362"],"URL":"https:\/\/doi.org\/10.1137\/060676362","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}