{"id":"https://openalex.org/W2025933665","doi":"https://doi.org/10.1109/isit.2012.6284267","title":"Capacity achieving linear codes with random binary sparse generating matrices over the Binary Symmetric Channel","display_name":"Capacity achieving linear codes with random binary sparse generating matrices over the Binary Symmetric Channel","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2025933665","doi":"https://doi.org/10.1109/isit.2012.6284267","mag":"2025933665"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6284267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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/A5034211674","display_name":"A. Makhdoumi Kakhaki","orcid":null},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["IR","US"],"is_corresponding":true,"raw_author_name":"A. Makhdoumi Kakhaki","raw_affiliation_strings":["Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","Department of EECS, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"Department of EECS, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049953632","display_name":"Hossein Karkeh Abadi","orcid":null},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["IR","US"],"is_corresponding":false,"raw_author_name":"H. Karkeh Abadi","raw_affiliation_strings":["Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","Department of EE, University of Stanford, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"Department of EE, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060929936","display_name":"Pedram Pad","orcid":"https://orcid.org/0000-0001-7764-2800"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","IR"],"is_corresponding":false,"raw_author_name":"P. Pad","raw_affiliation_strings":["Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","School of Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"School of Engineering, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030979044","display_name":"Hamid Saeedi","orcid":"https://orcid.org/0000-0003-2706-228X"},"institutions":[{"id":"https://openalex.org/I4210116604","display_name":"Ilam University","ror":"https://ror.org/01r277z15","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210116604"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"H. Saeedi","raw_affiliation_strings":["Department of ECE, Tarbiat Moalem University, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of ECE, Tarbiat Moalem University, Tehran, Iran","institution_ids":["https://openalex.org/I4210116604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069159448","display_name":"Farokh Marvasti","orcid":"https://orcid.org/0000-0002-4635-8986"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"F. Marvasti","raw_affiliation_strings":["Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062784300","display_name":"Kasra Alishahi","orcid":null},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"K. Alishahi","raw_affiliation_strings":["Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5034211674"],"corresponding_institution_ids":["https://openalex.org/I133529467","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.7092,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.71881389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"56","issue":null,"first_page":"621","last_page":"625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/binary-erasure-channel","display_name":"Binary erasure channel","score":0.8064420819282532},{"id":"https://openalex.org/keywords/binary-symmetric-channel","display_name":"Binary symmetric channel","score":0.6597036719322205},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.6125975847244263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5908211469650269},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.5810627937316895},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5423030257225037},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5271498560905457},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.507562518119812},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.486083060503006},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.48271796107292175},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4709630608558655},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.47040826082229614},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3978872299194336},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.2662518322467804},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1480986773967743},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08551537990570068}],"concepts":[{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.8064420819282532},{"id":"https://openalex.org/C173988684","wikidata":"https://www.wikidata.org/wiki/Q863510","display_name":"Binary symmetric channel","level":4,"score":0.6597036719322205},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.6125975847244263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5908211469650269},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.5810627937316895},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5423030257225037},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5271498560905457},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.507562518119812},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.486083060503006},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.48271796107292175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4709630608558655},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.47040826082229614},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3978872299194336},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.2662518322467804},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1480986773967743},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08551537990570068},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2012.6284267","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284267","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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":16,"referenced_works":["https://openalex.org/W1858818897","https://openalex.org/W1989008275","https://openalex.org/W1993944611","https://openalex.org/W2096667287","https://openalex.org/W2098480381","https://openalex.org/W2098666392","https://openalex.org/W2098917181","https://openalex.org/W2106864314","https://openalex.org/W2128765501","https://openalex.org/W2137787303","https://openalex.org/W2156938362","https://openalex.org/W2296125569","https://openalex.org/W2296600582","https://openalex.org/W2566505556","https://openalex.org/W2993383518","https://openalex.org/W4229922087"],"related_works":["https://openalex.org/W2502955786","https://openalex.org/W2162141500","https://openalex.org/W2142213376","https://openalex.org/W2975988509","https://openalex.org/W2538179194","https://openalex.org/W2739456797","https://openalex.org/W2991327005","https://openalex.org/W3098001956","https://openalex.org/W2972577883","https://openalex.org/W2987150391"],"abstract_inverted_index":{"In":[0,192],"this":[1],"paper,":[2],"we":[3,149,169],"prove":[4,170,211],"the":[5,19,27,35,40,55,63,82,86,97,117,120,124,134,171,189,196],"existence":[6,28,172,197],"of":[7,29,119,136,173,184,188,198,206,217],"capacity":[8,30,70,174,199,222],"achieving":[9,31,71,175,200,223],"linear":[10,32,158,176],"codes":[11,33,43,56,159,177],"with":[12,44,57,178,224],"random":[13,41],"binary":[14,42],"sparse":[15,51,58,201,218],"generating":[16,47,59,121,190,219],"matrices":[17,60,220],"over":[18],"Binary":[20,76],"Symmetric":[21],"Channel":[22],"(BSC).":[23],"The":[24],"results":[25,84],"on":[26,91,102,146,186],"in":[34,62,85],"literature":[36,64],"are":[37,65,89],"limited":[38],"to":[39,68,81,143,194,210],"equal":[45],"probability":[46,135],"matrix":[48,122],"elements":[49],"and":[50,106,123,165],"parity-check":[52],"matrices.":[53],"Moreover,":[54,168],"reported":[61],"not":[66],"proved":[67],"be":[69],"for":[72],"channels":[73],"other":[74],"than":[75],"Erasure":[77],"Channel.":[78],"As":[79],"opposed":[80],"existing":[83],"literature,":[87],"which":[88,129],"based":[90,101],"optimal":[92],"maximum":[93],"a":[94,103,152,161,179],"posteriori":[95],"decoders,":[96],"proposed":[98],"approach":[99],"is":[100,108,209,221],"different":[104],"decoder":[105],"consequently":[107],"suboptimal.":[109],"We":[110],"also":[111,150],"demonstrate":[112],"an":[113,203],"interesting":[114],"trade-off":[115],"between":[116],"sparsity":[118],"error":[125,137,166],"exponent":[126],"(a":[127],"constant":[128],"determines":[130],"how":[131],"exponentially":[132],"fast":[133],"decays":[138],"as":[139],"block":[140,163],"length":[141,164],"tends":[142],"infinity).":[144],"Based":[145],"our":[147,207],"results,":[148],"propose":[151],"channel":[153],"coding":[154],"rate":[155],"achievable":[156],"by":[157],"at":[160],"given":[162,180],"probability.":[167,226],"(arbitrarily":[181],"low)":[182],"density":[183],"ones":[185],"rows":[187],"matrix.":[191],"addition":[193],"proving":[195],"codes,":[202],"important":[204],"conclusion":[205],"paper":[208],"that":[212],"any":[213],"arbitrarily":[214],"selected":[215],"sequence":[216],"high":[225]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}