On network coding capacity : matroidal networks and network capacity regions
Name
713714210-MIT.pdf
Description
Full printable version
Size
3.72 MB
Format
Adobe PDF
Checksum (MD5)
fdc106670f068ee35ba8e817d5d8b663
Author(s)
Kim, Anthony Eli
Advisor(s)
Muriel Médard.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity regions. In our matroidal approach, we prove the converse of the theorem which states that, if a network is scalar-linearly solvable then it is a matroidal network associated with a representable matroid over a finite field. As a consequence, we obtain a correspondence between scalar-linearly solvable networks and representable matroids over finite fields in the framework of matroidal networks. We prove a theorem about the scalar-linear solvability of networks and field characteristics. We provide a method for generating scalar-linearly solvable networks that are potentially different from the networks that we already know are scalar-linearly solvable. In our capacity region approach, we define a multi-dimensional object, called the network capacity region, associated with networks that is analogous to the rate regions in information theory. For the network routing capacity region, we show that the region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. For the network linear coding capacity region, we construct a computable rational polytope, with respect to a given finite field, that inner bounds the linear coding capacity region and provide exact algorithms and approximation heuristics for computing the polytope. The exact algorithms and approximation heuristics we present are not polynomial time schemes and may depend on the output size.
Description
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 68-70).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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