{"id":"https://openalex.org/W4386057555","doi":"https://doi.org/10.1109/isit54713.2023.10206551","title":"Matrix Completion over Finite Fields: Bounds and Belief Propagation Algorithms","display_name":"Matrix Completion over Finite Fields: Bounds and Belief Propagation Algorithms","publication_year":2023,"publication_date":"2023-06-25","ids":{"openalex":"https://openalex.org/W4386057555","doi":"https://doi.org/10.1109/isit54713.2023.10206551"},"language":"en","primary_location":{"id":"doi:10.1109/isit54713.2023.10206551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206551","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084796282","display_name":"Mahdi Soleymani","orcid":"https://orcid.org/0000-0002-5495-901X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mahdi Soleymani","raw_affiliation_strings":["University of California San Diego,Hal&#x0131;c&#x0131;o&#x011F;lu Data Science Institute"],"affiliations":[{"raw_affiliation_string":"University of California San Diego,Hal&#x0131;c&#x0131;o&#x011F;lu Data Science Institute","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100409533","display_name":"Qiang Liu","orcid":"https://orcid.org/0000-0003-3171-1406"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiang Liu","raw_affiliation_strings":["University of Michigan Ann Arbor,Department of Electrical Engineering and Computer Science","Department of Electrical Engineering and Computer Science, University of Michigan Ann Arbor"],"affiliations":[{"raw_affiliation_string":"University of Michigan Ann Arbor,Department of Electrical Engineering and Computer Science","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan Ann Arbor","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056299839","display_name":"Hessam Mahdavifar","orcid":"https://orcid.org/0000-0001-9021-1992"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hessam Mahdavifar","raw_affiliation_strings":["University of Michigan Ann Arbor,Department of Electrical Engineering and Computer Science","Department of Electrical Engineering and Computer Science, University of Michigan Ann Arbor"],"affiliations":[{"raw_affiliation_string":"University of Michigan Ann Arbor,Department of Electrical Engineering and Computer Science","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan Ann Arbor","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029521003","display_name":"Laura Balzano","orcid":"https://orcid.org/0000-0003-2914-123X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Laura Balzano","raw_affiliation_strings":["University of Michigan Ann Arbor,Department of Electrical Engineering and Computer Science","Department of Electrical Engineering and Computer Science, University of Michigan Ann Arbor"],"affiliations":[{"raw_affiliation_string":"University of Michigan Ann Arbor,Department of Electrical Engineering and Computer Science","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan Ann Arbor","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5084796282"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.4018,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60992143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1166","last_page":"1171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5759372115135193},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5724389553070068},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5428135991096497},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.5408315062522888},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5379799604415894},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.5283371210098267},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.4570773243904114},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3459450602531433},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32634294033050537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28132981061935425},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24439260363578796},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1255987584590912},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09843006730079651},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07275164127349854},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.0704495906829834}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5759372115135193},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5724389553070068},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5428135991096497},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.5408315062522888},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5379799604415894},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.5283371210098267},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.4570773243904114},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3459450602531433},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32634294033050537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28132981061935425},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24439260363578796},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1255987584590912},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09843006730079651},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07275164127349854},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0704495906829834},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit54713.2023.10206551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206551","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1510028821","https://openalex.org/W1518885151","https://openalex.org/W1657130172","https://openalex.org/W1982114217","https://openalex.org/W2039528926","https://openalex.org/W2042792015","https://openalex.org/W2096642693","https://openalex.org/W2096667287","https://openalex.org/W2116471929","https://openalex.org/W2118550318","https://openalex.org/W2123051422","https://openalex.org/W2124608575","https://openalex.org/W2137813581","https://openalex.org/W2268674159","https://openalex.org/W2512153233","https://openalex.org/W2791947914","https://openalex.org/W2962961919","https://openalex.org/W2963549383","https://openalex.org/W2964170835","https://openalex.org/W3006030847","https://openalex.org/W3027308717","https://openalex.org/W3187534145","https://openalex.org/W4248101621","https://openalex.org/W4285296771","https://openalex.org/W4302028314","https://openalex.org/W6639729264","https://openalex.org/W6674909129","https://openalex.org/W6686278221","https://openalex.org/W6750408638"],"related_works":["https://openalex.org/W2963858139","https://openalex.org/W3118793956","https://openalex.org/W1530218127","https://openalex.org/W3099765941","https://openalex.org/W4301599454","https://openalex.org/W4232699667","https://openalex.org/W3081084973","https://openalex.org/W2054519467","https://openalex.org/W4300656036","https://openalex.org/W2964184729"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,18,25,38,41,56,60,73,78,101,105,143,159],"low":[3],"rank":[4],"matrix":[5,74,107,145],"completion":[6,75,108],"problem":[7,12,39,76,109],"over":[8,77,110],"finite":[9,79,111],"fields.":[10],"This":[11],"has":[13,119,146],"been":[14],"extensively":[15],"studied":[16],"in":[17,40,63,133],"domain":[19],"of":[20,27,81,113],"real/complex":[21],"numbers,":[22],"however,":[23],"to":[24,36,45,93,136],"best":[26],"authors\u2019":[28],"knowledge,":[29],"there":[30],"exists":[31],"merely":[32],"one":[33,103],"efficient":[34],"algorithm":[35,61,99],"tackle":[37],"binary":[42],"field,":[43],"due":[44],"Saunderson":[46],"et":[47],"al.":[48],"[1].":[49,64],"In":[50],"this":[51,95],"paper,":[52],"we":[53,66],"improve":[54],"upon":[55],"theoretical":[57],"guarantees":[58],"for":[59,72,104],"provided":[62],"Furthermore,":[65],"formulate":[67],"a":[68,87,120],"new":[69],"graphical":[70],"model":[71],"field":[80],"size":[82],"q,":[83],"${\\mathbb{F}_q}$,":[84],"and":[85,151],"present":[86],"message":[88],"passing":[89],"(MP)":[90],"based":[91],"approach":[92],"solve":[94],"problem.":[96],"The":[97],"proposed":[98,117],"is":[100],"first":[102],"considered":[106],"fields":[112],"arbitrary":[114],"size.":[115],"Our":[116],"method":[118],"significantly":[121],"lower":[122],"computational":[123],"complexity,":[124],"reducing":[125],"it":[126],"from":[127],"O(n":[128,137],"<sup":[129,138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[130,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2r+3</sup>":[131],")":[132,141],"[1]":[134],"down":[135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[140],"(where,":[142],"underlying":[144],"dimension":[147],"n":[148,150],"\u00d7":[149],"r":[152],"denotes":[153],"its":[154],"rank),":[155],"while":[156],"also":[157],"improving":[158],"performance.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}