Conference proceeding
Algorithms for Computing Network Coding Rate Regions via Single Element Extensions of Matroids
2014 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), pp.2306-2310
01 Jan 2014
Abstract
We propose algorithms for finding extreme rays of rate regions achievable with vector linear codes over finite fields F (q); q is an element of {2, 3, 4} for which there are known forbidden minors for matroid representability. We use the idea of single element extensions (SEEs) of matroids and enumeration of non-isomorphic matroids using SEEs, to first propose an algorithm to obtain lists of all non-isomorphic matroids representable over a given finite field. We modify this algorithm to produce only the list of all non-isomorphic connected matroids representable over the given finite field. We then integrate the process of testing which matroids in a list of matroids form valid linear network codes for a given network within matroid enumeration. We name this algorithm, which essentially builds all matroids that form valid network codes for a given network from scratch, as network-constrained matroid enumeration.
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Details
- Title
- Algorithms for Computing Network Coding Rate Regions via Single Element Extensions of Matroids
- Creators
- Jayant Apte - Drexel Univ, Dept ECE, Philadelphia, PA 19104 USACongduan Li - Drexel Univ, Dept ECE, Philadelphia, PA 19104 USAJohn MacLaren Walsh - Drexel UniversityIEEE
- Publication Details
- 2014 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), pp.2306-2310
- Conference
- 2014 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)
- Series
- IEEE International Symposium on Information Theory
- Publisher
- IEEE
- Number of pages
- 5
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- Electrical and Computer Engineering
- Identifiers
- 991019170565604721
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- Computer Science, Theory & Methods
- Engineering, Electrical & Electronic