Boosted KZ and LLL Algorithms
There exist two issues among popular lattice reduction algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reductio...
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| Veröffentlicht in: | IEEE transactions on signal processing 2017-09, Vol.65 (18), p.4784-4796 |
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| creator | Lyu, Shanxiang Ling, Cong |
| description | There exist two issues among popular lattice reduction algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reduction in terms of providing short basis vectors, despite its superior theoretical upper bounds. To address these limitations, we improve the size reduction steps in KZ and LLL to set up two new efficient algorithms, referred to as boosted KZ and LLL, for solving the shortest basis problem with exponential and polynomial complexity, respectively. Both of them offer better actual performance than their classic counterparts, and the performance bounds for KZ are also improved. We apply them to designing integer-forcing (IF) linear receivers for multi-input multioutput communications. Our simulations confirm their rate and complexity advantages. |
| doi_str_mv | 10.1109/TSP.2017.2708020 |
| format | Article |
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The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reduction in terms of providing short basis vectors, despite its superior theoretical upper bounds. To address these limitations, we improve the size reduction steps in KZ and LLL to set up two new efficient algorithms, referred to as boosted KZ and LLL, for solving the shortest basis problem with exponential and polynomial complexity, respectively. Both of them offer better actual performance than their classic counterparts, and the performance bounds for KZ are also improved. We apply them to designing integer-forcing (IF) linear receivers for multi-input multioutput communications. 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(IEEE) 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c291t-46cb832a256755020b28670c8ffba74f5436dcf93182b354e6ccd990caaf37c03</citedby><cites>FETCH-LOGICAL-c291t-46cb832a256755020b28670c8ffba74f5436dcf93182b354e6ccd990caaf37c03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7933198$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/7933198$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Lyu, Shanxiang</creatorcontrib><creatorcontrib>Ling, Cong</creatorcontrib><title>Boosted KZ and LLL Algorithms</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>There exist two issues among popular lattice reduction algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reduction in terms of providing short basis vectors, despite its superior theoretical upper bounds. To address these limitations, we improve the size reduction steps in KZ and LLL to set up two new efficient algorithms, referred to as boosted KZ and LLL, for solving the shortest basis problem with exponential and polynomial complexity, respectively. Both of them offer better actual performance than their classic counterparts, and the performance bounds for KZ are also improved. We apply them to designing integer-forcing (IF) linear receivers for multi-input multioutput communications. Our simulations confirm their rate and complexity advantages.</description><subject>Algorithm design and analysis</subject><subject>Algorithms</subject><subject>Codes</subject><subject>Complexity</subject><subject>Complexity theory</subject><subject>Computer simulation</subject><subject>integer-forcing</subject><subject>Lattice reduction</subject><subject>Lattices</subject><subject>Linear receivers</subject><subject>LLL</subject><subject>Matrix decomposition</subject><subject>MIMO</subject><subject>Receivers</subject><subject>shortest basis problem</subject><subject>Signal processing algorithms</subject><subject>Size reduction</subject><subject>Upper bounds</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1LAzEQhoMoWKt3QYQFz1tn8rFJjrXUD1xQsIJ4Cdlsoi1ttybbg__elBZPM4fnnZd5CLlEGCGCvp29vY4ooBxRCQooHJEBao4lcFkd5x0EK4WSH6fkLKUFAHKuqwG5vuu61Pu2eP4s7Lot6rouxsuvLs7771U6JyfBLpO_OMwheb-fziaPZf3y8DQZ16WjGvuSV65RjFoqKilELm-oqiQ4FUJjJQ-Cs6p1QTNUtGGC-8q5Vmtw1gYmHbAhudnf3cTuZ-tTbxbdNq5zpUGNGlDknzIFe8rFLqXog9nE-crGX4NgdhJMlmB2EsxBQo5c7SNz7_0_LjVjqBX7A2sTVPM</recordid><startdate>20170915</startdate><enddate>20170915</enddate><creator>Lyu, Shanxiang</creator><creator>Ling, Cong</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovász (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduction suffers worse performance than Minkowski reduction in terms of providing short basis vectors, despite its superior theoretical upper bounds. To address these limitations, we improve the size reduction steps in KZ and LLL to set up two new efficient algorithms, referred to as boosted KZ and LLL, for solving the shortest basis problem with exponential and polynomial complexity, respectively. Both of them offer better actual performance than their classic counterparts, and the performance bounds for KZ are also improved. We apply them to designing integer-forcing (IF) linear receivers for multi-input multioutput communications. Our simulations confirm their rate and complexity advantages.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TSP.2017.2708020</doi><tpages>13</tpages></addata></record> |
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| subjects | Algorithm design and analysis Algorithms Codes Complexity Complexity theory Computer simulation integer-forcing Lattice reduction Lattices Linear receivers LLL Matrix decomposition MIMO Receivers shortest basis problem Signal processing algorithms Size reduction Upper bounds |
| title | Boosted KZ and LLL Algorithms |
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