{"id":"https://openalex.org/W1965559626","doi":"https://doi.org/10.1109/tit.2014.2352296","title":"A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions","display_name":"A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions","publication_year":2014,"publication_date":"2014-08-28","ids":{"openalex":"https://openalex.org/W1965559626","doi":"https://doi.org/10.1109/tit.2014.2352296","mag":"1965559626"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2352296","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2352296","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1309.7910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Arvind Yedla","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101778","display_name":"Samsung (United States)","ror":"https://ror.org/01bfbvm65","country_code":"US","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210101778"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Arvind Yedla","raw_affiliation_strings":["Samsung Information Systems at San Diego, San Jose, CA, USA"],"affiliations":[{"raw_affiliation_string":"Samsung Information Systems at San Diego, San Jose, CA, USA","institution_ids":["https://openalex.org/I4210101778"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yung-Yih Jian","orcid":null},"institutions":[{"id":"https://openalex.org/I4210087596","display_name":"Qualcomm (United States)","ror":"https://ror.org/002zrf773","country_code":"US","type":"company","lineage":["https://openalex.org/I4210087596"]},{"id":"https://openalex.org/I4210111675","display_name":"Market Matters","ror":"https://ror.org/021yan307","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210111675"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yung-Yih Jian","raw_affiliation_strings":["Qualcomm Inc., Santa Clara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Qualcomm Inc., Santa Clara, CA, USA","institution_ids":["https://openalex.org/I4210087596","https://openalex.org/I4210111675"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Phong S. Nguyen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210154351","display_name":"Marvell (United States)","ror":"https://ror.org/04wmff902","country_code":"US","type":"company","lineage":["https://openalex.org/I4210092679","https://openalex.org/I4210154351"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Phong S. Nguyen","raw_affiliation_strings":["Marvell Semiconductor Inc., Santa Clara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Marvell Semiconductor Inc., Santa Clara, CA, USA","institution_ids":["https://openalex.org/I4210154351"]}]},{"author_position":"last","author":{"id":null,"display_name":"Henry D. Pfister","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Henry D. Pfister","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210101778"],"apc_list":null,"apc_paid":null,"fwci":8.2735,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.97620657,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"11","first_page":"6943","last_page":"6965"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9763000011444092,"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":0.9763000011444092,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.005200000014156103,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.0034000000450760126,"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":0.7091000080108643},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.6258999705314636},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5022000074386597},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.478300005197525},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.39419999718666077},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.3921000063419342},{"id":"https://openalex.org/keywords/convolutional-code","display_name":"Convolutional code","score":0.37709999084472656},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.3734999895095825},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.366100013256073}],"concepts":[{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.7091000080108643},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.6258999705314636},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5022000074386597},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.478300005197525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47029998898506165},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.37709999084472656},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.32739999890327454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.3154999911785126},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.28760001063346863},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.26969999074935913},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26579999923706055},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C33529081","wikidata":"https://www.wikidata.org/wiki/Q18378194","display_name":"Serial concatenated convolutional codes","level":5,"score":0.258899986743927}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2014.2352296","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2352296","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1309.7910","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.7910","pdf_url":"https://arxiv.org/pdf/1309.7910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1309.7910","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.7910","pdf_url":"https://arxiv.org/pdf/1309.7910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G273407139","display_name":null,"funder_award_id":"0747470","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3877322553","display_name":null,"funder_award_id":"0802124","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G555895826","display_name":null,"funder_award_id":"1320924","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W1536930200","https://openalex.org/W1554859668","https://openalex.org/W1557899381","https://openalex.org/W1974321276","https://openalex.org/W1980044712","https://openalex.org/W1980544482","https://openalex.org/W1991528082","https://openalex.org/W1994121055","https://openalex.org/W2001812907","https://openalex.org/W2018322127","https://openalex.org/W2022068191","https://openalex.org/W2024876346","https://openalex.org/W2034585717","https://openalex.org/W2058957447","https://openalex.org/W2073868986","https://openalex.org/W2076370927","https://openalex.org/W2076859597","https://openalex.org/W2082029531","https://openalex.org/W2090127253","https://openalex.org/W2103116189","https://openalex.org/W2111616148","https://openalex.org/W2115104320","https://openalex.org/W2116787460","https://openalex.org/W2117184753","https://openalex.org/W2117726335","https://openalex.org/W2117898372","https://openalex.org/W2118473837","https://openalex.org/W2123119950","https://openalex.org/W2129462326","https://openalex.org/W2137315663","https://openalex.org/W2143439424","https://openalex.org/W2146712141","https://openalex.org/W2155982084","https://openalex.org/W2156595614","https://openalex.org/W2156973751","https://openalex.org/W2156991284","https://openalex.org/W2157638198","https://openalex.org/W2164196863","https://openalex.org/W2164366353","https://openalex.org/W2165942867","https://openalex.org/W2166330961","https://openalex.org/W2170558200","https://openalex.org/W2170992065","https://openalex.org/W2172679141","https://openalex.org/W2179644698","https://openalex.org/W2570804843","https://openalex.org/W2571527823","https://openalex.org/W2610971674","https://openalex.org/W2962770701","https://openalex.org/W2963194516","https://openalex.org/W2963278042","https://openalex.org/W2963578263","https://openalex.org/W2963658019","https://openalex.org/W4292232932","https://openalex.org/W6640611811","https://openalex.org/W6640623458","https://openalex.org/W6668270486","https://openalex.org/W6714914520","https://openalex.org/W6729847528","https://openalex.org/W6785880612","https://openalex.org/W6979755570"],"related_works":[],"abstract_inverted_index":{"Low-density":[0],"parity-check":[1],"(LDPC)":[2],"convolutional":[3],"codes":[4,146,153,162,173],"(or":[5],"spatially":[6,51],"coupled":[7,52,83,97,111],"codes)":[8],"were":[9],"recently":[10],"shown":[11],"to":[12,55,78,127],"approach":[13,87],"capacity":[14],"on":[15,90,147,154,174],"the":[16,46,50,62,96,106,110,117,120,140,148,155,167,181],"binary":[17],"erasure":[18,178],"channel":[19],"(BEC)":[20],"and":[21,98,124,180],"binary-input":[22],"memoryless":[23],"symmetric":[24],"channels.":[25],"The":[26],"mechanism":[27],"behind":[28],"this":[29,66,128],"spectacular":[30],"performance":[31],"is":[32,43,88,113],"now":[33],"called":[34],"threshold":[35,48,59,74],"saturation":[36,75],"via":[37],"spatial":[38],"coupling.":[39],"This":[40],"new":[41],"phenomenon":[42,129],"characterized":[44],"by":[45,61,116],"belief-propagation":[47],"of":[49,73,82,109,119,135,159,171,184],"ensemble":[53],"increasing":[54],"an":[56],"intrinsic":[57],"noise":[58],"defined":[60],"uncoupled":[63,99,121],"system.":[64],"In":[65],"paper,":[67],"we":[68,125],"present":[69],"a":[70,79,157],"simple":[71],"proof":[72],"that":[76,105],"applies":[77],"wide":[80],"class":[81,158],"scalar":[84],"recursions.":[85,100],"Our":[86,101],"based":[89],"constructing":[91],"potential":[92,122],"functions":[93],"for":[94],"both":[95],"results":[102],"actually":[103],"show":[104],"fixed":[107],"point":[108],"recursion":[112],"essentially":[114],"determined":[115],"minimum":[118],"function":[123],"refer":[126],"as":[130],"Maxwell":[131],"saturation.":[132],"A":[133],"variety":[134],"examples":[136],"are":[137],"considered":[138],"including":[139],"density-evolution":[141],"equations":[142],"for:":[143],"irregular":[144,150],"LDPC":[145,161,172],"BEC,":[149,156],"low-density":[151],"generator-matrix":[152],"generalized":[160],"with":[163,177,187],"BCH":[164],"component":[165],"codes,":[166],"joint":[168],"iterative":[169],"decoding":[170],"intersymbol-interference":[175],"channels":[176],"noise,":[179],"compressed":[182],"sensing":[183],"random":[185],"vectors":[186],"independent":[188],"identically":[189],"distributed":[190],"components.":[191]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2016-06-24T00:00:00"}
