Adversarial network coding studies the transmission of data over networks affected by adversarial noise. In this realm, the noise is modeled by an omniscient adversary who is restricted to corrupting a proper subset of the network edges. In 2018, Ravagnani and Kschischang established a combinatorial framework for adversarial networks. The study was recently furthered by Beemer, Kilic and Ravagnani, with particular focus on the one-shot capacity: a measure of the maximum number of symbols that can be transmitted in a single use of the network without errors. In this thesis, both bounds and capacity-achieving schemes are provided for families of adversarial networks in multiple transmission rounds. We also demonstrate scenarios where we transmit more information using a network multiple times for communication versus using the network once. Some results in this thesis are joint work with Giuseppe Cotardo (Virginia Tech), Gretchen Matthews (Virginia Tech) and Alberto Ravagnani (Eindhoven University of Technology). / Master of Science / We study how to best transfer data across a communication network even if there is adversarial interference using network coding. Network coding is used in video streaming, autonomous vehicles, 5G and NextG communications, satellite networks, and Internet of Things (IoT) devices among other applications. It is the process that encodes data before sending it and decodes it upon receipt. It brings advantages such as increased network efficiency, improved reliability, reduced redundancy, enhanced resilience, and energy savings. We seek to enhance this valuable technique by determining optimal ways in which to utilize network coding schemes. We explore scenarios in which an adversary has partial access to a network. To examine the maximum data that can be communicated over one use of a network, we require the intermediate parts of the network process the information before forwarding it in a process called network decoding. In this thesis, we focus on characterizing when using a network multiple times for communication increases the amount of information that is received regardless of the worst-case adversarial attack, building on prior work that shows how underlying structure influences capacity. We design efficient methods for specific networks, to communicate at capacity.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/118924 |
| Date | 08 May 2024 |
| Creators | Shapiro, Julia Marie |
| Contributors | Mathematics, Matthews, Gretchen L., Lopez Valdez, Hiram Habid, Shimozono, Mark M. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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