On Field Size and Success Probability in Network Coding

Hans Olav Geil; Ryutaroh Matsumoto; Casper Thomsen

doi:10.1007/978-3-540-69499-1_14

On Field Size and Success Probability in Network Coding

Hans Olav Geil, Ryutaroh Matsumoto, Casper Thomsen

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

4 Citationer (Scopus)

Abstract

Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.

Originalsprog	Engelsk
Titel	Arithmetic of Finite Fields : 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings
Forlag	Springer
Publikationsdato	2008
Sider	157-173
ISBN (Trykt)	978-3-540-69498-4
DOI	https://doi.org/10.1007/978-3-540-69499-1_14
Status	Udgivet - 2008
Begivenhed	International Workshop, WAIFI 2008 - Siena, Italien Varighed: 6 jul. 2008 → 9 jul. 2008 Konferencens nummer: 2

Konference

Konference	International Workshop, WAIFI 2008
Nummer	2
Land/Område	Italien
By	Siena
Periode	06/07/2008 → 09/07/2008

Navn	Lecture Notes in Computer Science
Nummer	5130
ISSN	0302-8743

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10.1007/978-3-540-69499-1_14

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Citationsformater

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title = "On Field Size and Success Probability in Network Coding",

abstract = "Using tools from algebraic geometry and Gr{\"o}bner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.",

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Geil, HO, Matsumoto, R & Thomsen, C 2008, On Field Size and Success Probability in Network Coding. i Arithmetic of Finite Fields: 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings. Springer, Lecture Notes in Computer Science, nr. 5130, s. 157-173, International Workshop, WAIFI 2008, Siena, Italien, 06/07/2008. https://doi.org/10.1007/978-3-540-69499-1_14

On Field Size and Success Probability in Network Coding. / Geil, Hans Olav; Matsumoto, Ryutaroh; Thomsen, Casper.
Arithmetic of Finite Fields: 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings. Springer, 2008. s. 157-173 (Lecture Notes in Computer Science; Nr. 5130).

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › peer review

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N2 - Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.

AB - Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.

U2 - 10.1007/978-3-540-69499-1_14

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M3 - Article in proceeding

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ER -

On Field Size and Success Probability in Network Coding

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