{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/86840"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/86840","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"A Structural Study of Network Coding Through the Lens of Group Theory","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Wei, Fei; 0000-0002-8943-0335"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Langberg, Michael","Electrical Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-02-25T23:23:19Z","date_published":"2025-02-25T23:23:19Z","updated_at":"2026-07-27T19:05:37Z","subjects":["electrical engineering"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/86840","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Langberg, Michael","Electrical Engineering"]},{"key":"dc:creator","label":"Author","values":["Wei, Fei; 0000-0002-8943-0335"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-02-25T23:23:19Z","2020","2020-08-18 10:31:38"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["electrical engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/86840"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","Network coding is a network communication scheme which deploys encoding at intermediate nodes, and can significantly improve the network throughput. In this thesis, we study the network coding paradigm through the lens of algebraic group theory. Specifically, we study the notion of \"group network codes\" and in particular their performance in the context of the \"edge removal problem\". Group network codes are a special family of network coding schemes that are associated with an algebraic (group) structure. Group network codes generalize linear codes, however, unlike linear codes, are known to be (approximately) optimal in the sense that any network coding scheme can be approximated by a group network coding scheme. While group network codes offer an algebraically structured alternative to general coding schemes, not much is known on this special family of codes. In this thesis, we seek to better understand group network codes. Specifically, we present certain structural properties of group network codes (e.g., their error probability), alternative formalizations for Abelian group network codes (that resemble the operational formalization of linear codes), and we study group network codes in the context of the edge removal problem. The edge removal problem is a fundamental problem in network coding, which studies the impact on achievable source rates (capacity region) when a communication edge is removed from a given network. The edge removal problem is understood on a handful of special network instances and network coding schemes, however, similar to the explicit characterization of the network coding capacity region for general networks, which remains widely open, the edge removal problem in full generality is not well understood and is open as well. The optimality of group network codes gives rise to the possibility that it is sufficient to understand the edge removal problem when restricted to the context of group network codes in order to understand the edge removal problem in full generality. In this thesis, we study the edge removal problem in the context of group network codes. We solve the edge removal problem for Abelian group network codes (a class of group codes defined with Abelian groups), we show that solving the edge removal problem reduces to the problem of modifying given coding schemes in such a way that preserves rate while adding an algebraic group structure to very localized parts of the network, and extend these results in an axiomatic manner beyond group codes to more general families of encoding functions. The results presented in this thesis appear in part in: 1. Wei, Fei, and Michael Langberg. \"The Effect of Removing a Network Communication Edge: Group Network Codes.\" 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2017.2. Wei, Fei, Michael Langberg, and Michelle Effros. \"A Local Perspective on the Edge Removal Problem.\" 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019.3. Wei, Fei, Michael Langberg, and Michelle Effros. \"Towards an Operational Definition of Group Network Codes.\" arXiv preprint arXiv:2002.00781 (2020).","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A Structural Study of Network Coding Through the Lens of Group Theory"]}]}],"canonical_facts":{"dc:contributor":["Langberg, Michael","Electrical Engineering"],"dc:creator":["Wei, Fei; 0000-0002-8943-0335"],"dc:date":["2025-02-25T23:23:19Z","2020","2020-08-18 10:31:38"],"dc:description":["Ph.D.","Network coding is a network communication scheme which deploys encoding at intermediate nodes, and can significantly improve the network throughput. In this thesis, we study the network coding paradigm through the lens of algebraic group theory. Specifically, we study the notion of \"group network codes\" and in particular their performance in the context of the \"edge removal problem\". Group network codes are a special family of network coding schemes that are associated with an algebraic (group) structure. Group network codes generalize linear codes, however, unlike linear codes, are known to be (approximately) optimal in the sense that any network coding scheme can be approximated by a group network coding scheme. While group network codes offer an algebraically structured alternative to general coding schemes, not much is known on this special family of codes. In this thesis, we seek to better understand group network codes. Specifically, we present certain structural properties of group network codes (e.g., their error probability), alternative formalizations for Abelian group network codes (that resemble the operational formalization of linear codes), and we study group network codes in the context of the edge removal problem. The edge removal problem is a fundamental problem in network coding, which studies the impact on achievable source rates (capacity region) when a communication edge is removed from a given network. The edge removal problem is understood on a handful of special network instances and network coding schemes, however, similar to the explicit characterization of the network coding capacity region for general networks, which remains widely open, the edge removal problem in full generality is not well understood and is open as well. The optimality of group network codes gives rise to the possibility that it is sufficient to understand the edge removal problem when restricted to the context of group network codes in order to understand the edge removal problem in full generality. In this thesis, we study the edge removal problem in the context of group network codes. We solve the edge removal problem for Abelian group network codes (a class of group codes defined with Abelian groups), we show that solving the edge removal problem reduces to the problem of modifying given coding schemes in such a way that preserves rate while adding an algebraic group structure to very localized parts of the network, and extend these results in an axiomatic manner beyond group codes to more general families of encoding functions. The results presented in this thesis appear in part in: 1. Wei, Fei, and Michael Langberg. \"The Effect of Removing a Network Communication Edge: Group Network Codes.\" 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2017.2. Wei, Fei, Michael Langberg, and Michelle Effros. \"A Local Perspective on the Edge Removal Problem.\" 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019.3. Wei, Fei, Michael Langberg, and Michelle Effros. \"Towards an Operational Definition of Group Network Codes.\" arXiv preprint arXiv:2002.00781 (2020).","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/86840"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["electrical engineering"],"dc:title":["A Structural Study of Network Coding Through the Lens of Group Theory"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:37Z"}