{"id":"https://openalex.org/W1618667235","doi":"https://doi.org/10.1109/isit.2007.4557333","title":"Existence Proofs of Some EXIT Like Functions","display_name":"Existence Proofs of Some EXIT Like Functions","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W1618667235","doi":"https://doi.org/10.1109/isit.2007.4557333","mag":"1618667235"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2007.4557333","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2007.4557333","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/118614","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080117292","display_name":"Vishwambhar Rathi","orcid":null},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Vishwambhar Rathi","raw_affiliation_strings":["School of Computer and Communication Sciences, EPF Lausanne, Switzerland","[EPFL Lausanne]"],"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Sciences, EPF Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"[EPFL Lausanne]","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058759310","display_name":"R\u00fcdiger Urbanke","orcid":"https://orcid.org/0000-0002-4839-821X"},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Ruediger Urbanke","raw_affiliation_strings":["School of Computer and Communication Sciences, EPF Lausanne, Switzerland","[EPFL Lausanne]"],"affiliations":[{"raw_affiliation_string":"School of Computer and Communication Sciences, EPF Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"[EPFL Lausanne]","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080117292"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.6732,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72883768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"866","last_page":"870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9980000257492065,"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":0.9941999912261963,"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/mathematical-proof","display_name":"Mathematical proof","score":0.728428840637207},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5317410826683044},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.5292560458183289},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5278111696243286},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.49950575828552246},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4582667946815491},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44895848631858826},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.43628543615341187},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4340939223766327},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.352121502161026},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.328045129776001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3098684549331665},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08441442251205444},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07087519764900208}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.728428840637207},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5317410826683044},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.5292560458183289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5278111696243286},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.49950575828552246},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4582667946815491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44895848631858826},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.43628543615341187},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4340939223766327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.352121502161026},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.328045129776001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3098684549331665},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08441442251205444},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07087519764900208},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/isit.2007.4557333","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2007.4557333","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.311.2403","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.2403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0704.2544v1.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:118614","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/118614","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:118614","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/20338","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:118614","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/118614","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1585814328","https://openalex.org/W1604254207","https://openalex.org/W2087922082","https://openalex.org/W2093288326","https://openalex.org/W2114468914","https://openalex.org/W2138644568","https://openalex.org/W2146712141","https://openalex.org/W2169732368","https://openalex.org/W4301236970","https://openalex.org/W6635159523","https://openalex.org/W6636095303","https://openalex.org/W6680619003","https://openalex.org/W6682055866"],"related_works":["https://openalex.org/W2072016134","https://openalex.org/W2351168932","https://openalex.org/W2465690287","https://openalex.org/W2376389741","https://openalex.org/W2108143034","https://openalex.org/W1997850251","https://openalex.org/W2084549431","https://openalex.org/W2011718785","https://openalex.org/W913430005","https://openalex.org/W1509695971"],"abstract_inverted_index":{"The":[0,49,89],"extended":[1],"BP":[2],"(EBP)":[3],"generalized":[4],"EXIT":[5,83],"(GEXIT)":[6],"function":[7,42],"introduced":[8],"in":[9,19,65,86],"C.":[10],"Measson":[11],"et":[12],"al.":[13],"(2005)":[14],"plays":[15],"a":[16],"fundamental":[17],"role":[18],"the":[20,30,35,39,57,60,80,93],"asymptotic":[21],"analysis":[22,73],"of":[23,38,59,82],"sparse":[24],"graph":[25],"codes.":[26],"For":[27],"transmission":[28],"over":[29],"binary":[31],"erasure":[32],"channel":[33],"(BEC)":[34],"analytic":[36],"properties":[37],"EBP":[40],"GEXIT":[41],"are":[43],"relatively":[44],"simple":[45],"and":[46,55],"well":[47],"understood.":[48],"general":[50],"case":[51],"is":[52,62,92],"much":[53],"harder":[54],"even":[56],"existence":[58,81],"curve":[61],"not":[63],"known":[64],"general.":[66],"We":[67],"introduce":[68],"some":[69,87],"tools":[70],"from":[71],"non-linear":[72],"which":[74],"can":[75],"be":[76],"useful":[77],"to":[78],"prove":[79],"like":[84],"curves":[85],"cases.":[88],"main":[90],"tool":[91],"Krasnoselskii-Rabinowitz":[94],"(KR)":[95],"bifurcation":[96],"theorem.":[97]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
