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

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

4 Citations (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.

Original language	English
Title of host publication	Arithmetic of Finite Fields : 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings
Publisher	Springer
Publication date	2008
Pages	157-173
ISBN (Print)	978-3-540-69498-4
DOIs	https://doi.org/10.1007/978-3-540-69499-1_14
Publication status	Published - 2008
Event	International Workshop, WAIFI 2008 - Siena, Italy Duration: 6 Jul 2008 → 9 Jul 2008 Conference number: 2

Conference

Conference	International Workshop, WAIFI 2008
Number	2
Country/Territory	Italy
City	Siena
Period	06/07/2008 → 09/07/2008

Series	Lecture Notes in Computer Science
Number	5130
ISSN	0302-8743

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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.",

author = "Geil, {Hans Olav} and Ryutaroh Matsumoto and Casper Thomsen",

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language = "English",

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series = "Lecture Notes in Computer Science",

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Geil, HO, Matsumoto, R & Thomsen, C 2008, On Field Size and Success Probability in Network Coding. in Arithmetic of Finite Fields: 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings. Springer, Lecture Notes in Computer Science, no. 5130, pp. 157-173, International Workshop, WAIFI 2008, Siena, Italy, 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. p. 157-173 (Lecture Notes in Computer Science; No. 5130).

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - On Field Size and Success Probability in Network Coding

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AU - Matsumoto, Ryutaroh

AU - Thomsen, Casper

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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

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

M3 - Article in proceeding

SN - 978-3-540-69498-4

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BT - Arithmetic of Finite Fields

PB - Springer

T2 - International Workshop, WAIFI 2008

Y2 - 6 July 2008 through 9 July 2008

ER -

On Field Size and Success Probability in Network Coding

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