{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80996"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80996","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Information Theoretic Limits for Secure Multimedia and Magnetic Recording","abstract":"The second part of this thesis addresses the problem of finding the capacity of two-dimensional (1, infinity) constrained channels for a binary alphabet. The Shannon capacity of a constrained channel is generalized to a notion of soft capacity which allows violations of the constraint. By drawing an analogy with an Ising array of the same geometry, it is proven that finding the soft capacity is equivalent to finding the partition function of the Ising model. Therefore, the problem of finding the capacity of a two-dimensional (1, infinity) constrained channel is reduced to the problem of finding an eigenvalue of a matrix.","abstract_html":"The second part of this thesis addresses the problem of finding the capacity of two-dimensional (1, infinity) constrained channels for a binary alphabet. The Shannon capacity of a constrained channel is generalized to a notion of soft capacity which allows violations of the constraint. By drawing an analogy with an Ising array of the same geometry, it is proven that finding the soft capacity is equivalent to finding the partition function of the Ising model. Therefore, the problem of finding the capacity of a two-dimensional (1, infinity) constrained channel is reduced to the problem of finding an eigenvalue of a matrix.","abstract_has_math":false,"creators":["Kiyavash, Negar"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":["Blahut, Richard E."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:09:09Z","date_published":"2015-09-25T20:09:09Z","updated_at":"2026-07-22T22:26:15Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3250272"],"render_values":[{"text":"(MiAaPQ)AAI3250272","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80996","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Blahut, Richard E."]},{"key":"dc:creator","label":"Author","values":["Kiyavash, Negar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:09:09Z","10000-01-01","2006"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/80996","(MiAaPQ)AAI3250272"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The second part of this thesis addresses the problem of finding the capacity of two-dimensional (1, infinity) constrained channels for a binary alphabet. 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