Characteristic-Dependent Linear Rank Inequalities With Applications to Network Coding
Two characteristic-dependent linear rank inequalities are given for eight variables. In particular, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three. The second inequality holds for all finite fields whose chara...
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| Published in | IEEE transactions on information theory Vol. 61; no. 5; pp. 2510 - 2530 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.05.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9448 1557-9654 |
| DOI | 10.1109/TIT.2015.2403361 |
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| Abstract | Two characteristic-dependent linear rank inequalities are given for eight variables. In particular, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three. The second inequality holds for all finite fields whose characteristic is three and does not in general hold over characteristics other than three. Applications of these inequalities to the computation of capacity upper bounds in network coding are demonstrated. |
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| AbstractList | Two characteristic-dependent linear rank inequalities are given for eight variables. In particular, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three. The second inequality holds for all finite fields whose characteristic is three and does not in general hold over characteristics other than three. Applications of these inequalities to the computation of capacity upper bounds in network coding are demonstrated. |
| Author | Zeger, Kenneth Dougherty, Randall Freiling, Eric |
| Author_xml | – sequence: 1 givenname: Randall surname: Dougherty fullname: Dougherty, Randall email: rdough@ccrwest.org organization: Center for Commun. Res., San Diego, CA, USA – sequence: 2 givenname: Eric surname: Freiling fullname: Freiling, Eric email: efreiling@gmail.com organization: Dept. of Electr. & Comput. Eng., Univ. of California at San Diego, La Jolla, CA, USA – sequence: 3 givenname: Kenneth surname: Zeger fullname: Zeger, Kenneth email: zeger@ucsd.edu organization: Dept. of Electr. & Comput. Eng., Univ. of California at San Diego, La Jolla, CA, USA |
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| SubjectTerms | capacity Coding theory Cramer-Rao bounds Electrical engineering Encoding Inequality Network coding Random variables Shannon entropy Upper bound Variables vector spaces Vectors |
| Title | Characteristic-Dependent Linear Rank Inequalities With Applications to Network Coding |
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