{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/130060"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/130060","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"List decoding expander-based codes via fast approximation of expanding CSPs","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","abstract_has_math":false,"creators":["Singh, Aman"],"institution":"University of Illinois Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Granha Jeronimo, Fernando"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-24","date_published":"2025-07-24","updated_at":"2026-07-22T22:25:06Z","subjects":["Coding Theory","Expander Codes","Regularity","List Decoding"],"languages":["en","eng"],"rights":["Copyright 2025 Aman Singh"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/130060","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Granha Jeronimo, Fernando"]},{"key":"dc:creator","label":"Author","values":["Singh, Aman"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-24","2025-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Coding Theory","Expander Codes","Regularity","List Decoding"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Aman Singh"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/130060"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","The student, Aman Singh, accepted the attached license on 2025-07-23 at 14:54.","The student, Aman Singh, submitted this Thesis for approval on 2025-07-23 at 15:03.","This Thesis was approved for publication on 2025-07-24 at 08:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22686 on 2025-10-21 at 10:06:18","We present near-linear time list decoding algorithms (in the block-length $n$) for expander-based code constructions. More precisely, we show that \\begin{itemize} \\item[(i)] For every $\\delta \\in (0,1)$ and $\\epsilon > 0$, there is an explicit family of good Tanner LDPC codes of (design) distance $\\delta$ that is $(\\delta - \\epsilon, O_\\varepsilon(1))$ list decodable in time $\\widetilde{\\mathcal{O}}_{\\varepsilon}(n)$ with alphabet size $O_\\delta(1)$, \\item[(ii)] For every $R \\in (0,1)$ and $\\epsilon > 0$, there is an explicit family of AEL codes of rate $R$, distance $1-R -\\varepsilon$ that is $(1-R-\\epsilon, O_\\varepsilon(1))$ list decodable in time $\\widetilde{\\mathcal{O}}_{\\varepsilon}(n)$ with alphabet size $\\exp(\\poly(1/\\epsilon))$, and \\item[(iii)] For every $R \\in (0,1)$ and $\\epsilon > 0$, there is an explicit family of AEL codes of rate $R$, distance $1-R-\\varepsilon$ that is $(1-R-\\epsilon, O(1/\\epsilon))$ list decodable in time $\\widetilde{\\mathcal{O}}_{\\varepsilon}(n)$ with alphabet size $\\exp(\\exp(\\poly(1/\\epsilon)))$ using recent near-optimal list size bounds from~\\cite{JMST25}. \\end{itemize} Our results are obtained by phrasing the decoding task as an agreement CSP \\cite{RWZ20,DinurHKNT19} on expander graphs and using the fast approximation algorithm for $q$-ary expanding CSPs from~\\cite{Jer23}, which is based on weak regularity decomposition. Similarly to list decoding $q$-ary Ta-Shma's codes in~\\cite{Jer23}, we show that it suffices to enumerate over assignments that are constant in each part (of the constantly many) of the decomposition in order to recover all codewords in the list."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["List decoding expander-based codes via fast approximation of expanding CSPs"]}]}],"canonical_facts":{"dc:contributor":["Granha Jeronimo, Fernando"],"dc:creator":["Singh, Aman"],"dc:date":["2025-07-24","2025-08"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","The student, Aman Singh, accepted the attached license on 2025-07-23 at 14:54.","The student, Aman Singh, submitted this Thesis for approval on 2025-07-23 at 15:03.","This Thesis was approved for publication on 2025-07-24 at 08:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22686 on 2025-10-21 at 10:06:18","We present near-linear time list decoding algorithms (in the block-length $n$) for expander-based code constructions. More precisely, we show that \\begin{itemize} \\item[(i)] For every $\\delta \\in (0,1)$ and $\\epsilon > 0$, there is an explicit family of good Tanner LDPC codes of (design) distance $\\delta$ that is $(\\delta - \\epsilon, O_\\varepsilon(1))$ list decodable in time $\\widetilde{\\mathcal{O}}_{\\varepsilon}(n)$ with alphabet size $O_\\delta(1)$, \\item[(ii)] For every $R \\in (0,1)$ and $\\epsilon > 0$, there is an explicit family of AEL codes of rate $R$, distance $1-R -\\varepsilon$ that is $(1-R-\\epsilon, O_\\varepsilon(1))$ list decodable in time $\\widetilde{\\mathcal{O}}_{\\varepsilon}(n)$ with alphabet size $\\exp(\\poly(1/\\epsilon))$, and \\item[(iii)] For every $R \\in (0,1)$ and $\\epsilon > 0$, there is an explicit family of AEL codes of rate $R$, distance $1-R-\\varepsilon$ that is $(1-R-\\epsilon, O(1/\\epsilon))$ list decodable in time $\\widetilde{\\mathcal{O}}_{\\varepsilon}(n)$ with alphabet size $\\exp(\\exp(\\poly(1/\\epsilon)))$ using recent near-optimal list size bounds from~\\cite{JMST25}. \\end{itemize} Our results are obtained by phrasing the decoding task as an agreement CSP \\cite{RWZ20,DinurHKNT19} on expander graphs and using the fast approximation algorithm for $q$-ary expanding CSPs from~\\cite{Jer23}, which is based on weak regularity decomposition. Similarly to list decoding $q$-ary Ta-Shma's codes in~\\cite{Jer23}, we show that it suffices to enumerate over assignments that are constant in each part (of the constantly many) of the decomposition in order to recover all codewords in the list."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/130060"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Aman Singh"],"dc:subject":["Coding Theory","Expander Codes","Regularity","List Decoding"],"dc:title":["List decoding expander-based codes via fast approximation of expanding CSPs"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}