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dc.contributor.advisorGeorghiades, Costas N.en_US
dc.contributor.advisorSprintson, Alexanderen_US
dc.creatorEl Rouayheb, Salim Y.en_US
dc.date.accessioned2011-02-22T22:23:46Zen_US
dc.date.accessioned2011-02-22T23:45:45Z
dc.date.available2011-02-22T22:23:46Zen_US
dc.date.available2011-02-22T23:45:45Z
dc.date.created2009-12en_US
dc.date.issued2011-02-22en_US
dc.date.submittedDecember 2009en_US
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7364en_US
dc.description.abstractSince its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks. Traditionally, information transmitted in a communication network was treated as a commodity in a transportation network, much like cars on highways or fluids in pipes. This approach, however, fails to capture the very nature of information, which in contrast to material goods, can be coded and decoded. The network coding techniques take full advantage of the inherent properties of information, and allow the nodes in a network, not only to store and forward, but also to "mix", i.e., encode, their received data. This approach was shown to result in a substantial throughput gain over the traditional routing and tree packing techniques. In this dissertation, we study applications of network coding for guarantying reliable and secure information transmission in networks with compromised edges. First, we investigate the construction of robust network codes for achieving network resilience against link failures. We focus on the practical important case of unicast networks with non-uniform edge capacities where a single link can fail at a time. We demonstrate that these networks exhibit unique structural properties when they are minimal, i.e., when they do not contain redundant edges. Based on this structure, we prove that robust linear network codes exist for these networks over GF(2), and devise an efficient algorithm to construct them. Second, we consider the problem of securing a multicast network against an eavesdropper that can intercept the packets on a limited number of network links. We recast this problem as a network generalization of the classical wiretap channel of Type II introduced by Ozarow and Wyner in 1984. In particular, we demonstrate that perfect secrecy can be achieved by using the Ozarow-Wyner scheme of coset coding at the source, on top of the implemented network code. Consequently, we transparently recover important results available in the literature on secure network coding. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction. In the last part of this dissertation, we study the connection between index coding, network coding, and matroid linear representation. We devise a reduction from the index coding problem to the network coding problem, implying that in the linear case these two problems are equivalent. We also present a second reduction from the matroid linear representability problem to index coding, and therefore, to network coding. The latter reduction establishes a strong connection between matroid theory and network coding theory. These two reductions are then used to construct special instances of the index coding problem where vector linear codes outperform scalar linear ones, and where non-linear encoding is needed to achieve the optimal number of transmission. Thereby, we provide a counterexample to a related conjecture in the literature and demonstrate the benefits of vector linear codes.en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.subjectNetwork Codingen_US
dc.subjectIndex Codingen_US
dc.subjectMatroid Theoryen_US
dc.subjectCommunicationsen_US
dc.titleNetwork and Index Coding with Application to Robust and Secure Communicationsen_US
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentElectrical and Computer Engineeringen_US
thesis.degree.disciplineElectrical Engineeringen_US
thesis.degree.grantorTexas A&M Universityen_US
thesis.degree.nameDoctor of Philosophyen_US
thesis.degree.levelDoctoralen_US
dc.contributor.committeeMemberDatta, Aniruddhaen_US
dc.contributor.committeeMemberChamberland, Jean-Francoisen_US
dc.contributor.committeeMemberRojas, J. Mauriceen_US
dc.type.genreElectronic Dissertationen_US
dc.type.materialtexten_US


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