國立虎尾科技大學 |

Local and Global Computation on Algebraic Data.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Local and Global Computation on Algebraic Data./
作者:	Gandikota, Venkata Surya Srikanth.
面頁冊數:	1 online resource (152 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.
標題:	Computer science. -
電子資源:	click for full text (PQDT)
ISBN:	9780355255089

Local and Global Computation on Algebraic Data.
Gandikota, Venkata Surya Srikanth.

Local and Global Computation on Algebraic Data. - 1 online resource (152 pages)

Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.

Thesis (Ph.D.)--Purdue University, 2017.

Includes bibliographical references

Point lattices and error-correcting codes are algebraic structures with numerous applications in communication, storage, and cryptography. In this dissertation we study error-correcting codes and lattices in the following models: classical global models, in which the algorithm can access its entire input, and local models, in which the algorithm has partial access to its input. We design fast algorithms that can reliably recover data from adversarial noise corruption, and show fundamental limitations of computation in these models.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355255089Subjects--Topical Terms:

573171
Computer science.
Index Terms--Genre/Form:

554714
Electronic books.

Local and Global Computation on Algebraic Data.
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264 0 $c 2017
300 $a 1 online resource (152 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.
500 $a Adviser: Elena Grigorescu.
502 $a Thesis (Ph.D.)--Purdue University, 2017.
504 $a Includes bibliographical references
520 $a Point lattices and error-correcting codes are algebraic structures with numerous applications in communication, storage, and cryptography. In this dissertation we study error-correcting codes and lattices in the following models: classical global models, in which the algorithm can access its entire input, and local models, in which the algorithm has partial access to its input. We design fast algorithms that can reliably recover data from adversarial noise corruption, and show fundamental limitations of computation in these models.
520 $a The challenging problems in coding theory revolve around the following nearest- neighbor search abstraction: given a collection of points with some special properties, and a target point, find a special point close to the target. In our case, the collection of special points form lattices or error-correcting codes, and the search problems refer to notions of decoding to a near lattice point, or a near codeword. Some well-known examples, which we also study here in local or global variants, include the Closest Vector Problem, and Bounded Distance Decoding problems.
520 $a In the global model, we propose efficient algorithms for solving the Closest Vector Problem in some special Construction-A lattices, a problem known to be hard in general. Further, we make progress on a long-standing open problem regarding decoding Reed-Solomon codes, by showing NP-hardness results for an asymptotic noise range.
520 $a Motivated by applications to linear programming and cryptography, we propose the notion of local testing for membership in point lattices, extending the classical notion of local testing for error-correcting codes to the Euclidean space. We design local algorithms for classical families of lattices and show several impossibility results.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Computer science. $3 573171
655 7 $a Electronic books. $2 local $3 554714
690 $a 0984
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Purdue University. $b Computer Sciences. $3 1179390
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10615637 $z click for full text (PQDT)