{"id":"https://openalex.org/W1942012113","doi":"https://doi.org/10.48550/arxiv.1301.5676","title":"Spatial Coupling as a Proof Technique","display_name":"Spatial Coupling as a Proof Technique","publication_year":2013,"publication_date":"2013-01-24","ids":{"openalex":"https://openalex.org/W1942012113","doi":"https://doi.org/10.48550/arxiv.1301.5676","mag":"1942012113"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1301.5676","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.5676","pdf_url":"https://arxiv.org/pdf/1301.5676","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1301.5676","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054397051","display_name":"Andrei Giurgiu","orcid":null,"observed_orcids":[]},"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":"Giurgiu, Andrei","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne,","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038854134","display_name":"Nicolas Macris","orcid":"https://orcid.org/0000-0003-2189-7411","observed_orcids":["https://orcid.org/0000-0003-2189-7411"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Macris, Nicolas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058759310","display_name":"Rudiger L. Urbanke","orcid":"https://orcid.org/0000-0002-4839-821X","observed_orcids":["https://orcid.org/0000-0002-4839-821X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Urbanke, R\u00fcdiger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9984999895095825,"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":0.9984999895095825,"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/T11130","display_name":"Coding theory and cryptography","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spatial-coupling","display_name":"spatial coupling","score":0.9800000190734863},{"id":"https://openalex.org/keywords/interpolation-methods","display_name":"interpolation methods","score":0.8059999942779541},{"id":"https://openalex.org/keywords/low-density-parity-check-codes","display_name":"LDPC codes","score":0.9729999899864197},{"id":"https://openalex.org/keywords/probabilistic-graphical-models","display_name":"probabilistic graphical models","score":0.7269999980926514},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"conditional entropy","score":0.8339999914169312},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"belief propagation","score":0.8199999928474426},{"id":"https://openalex.org/keywords/replica-symmetry","display_name":"replica symmetry","score":0.5680000185966492},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"asymptotic analysis","score":0.4740000069141388},{"id":"https://openalex.org/keywords/error-correcting-codes","display_name":"error-correcting codes","score":0.5640000104904175}],"concepts":[{"id":"https://openalex.org/C2775937380","wikidata":"https://www.wikidata.org/wiki/Q1232589","display_name":"Replica","level":2,"score":0.5729150772094727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.524389922618866},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5112566947937012},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5051293969154358},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4817954897880554},{"id":"https://openalex.org/C167927819","wikidata":"https://www.wikidata.org/wiki/Q1930567","display_name":"Shuffling","level":2,"score":0.4459286630153656},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4253312945365906},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.41871780157089233},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3731561303138733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.299407958984375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1848638951778412},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18114745616912842},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1410294473171234},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1301.5676","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.5676","pdf_url":"https://arxiv.org/pdf/1301.5676","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.766.9791","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.9791","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/1301.5676.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1301.5676","doi":"https://doi.org/10.48550/arxiv.1301.5676","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1301.5676","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1301.5676","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.5676","pdf_url":"https://arxiv.org/pdf/1301.5676","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W179407972","https://openalex.org/W1536930200","https://openalex.org/W1578462792","https://openalex.org/W1967744239","https://openalex.org/W1974321276","https://openalex.org/W1991528082","https://openalex.org/W2019194947","https://openalex.org/W2031852134","https://openalex.org/W2058957447","https://openalex.org/W2077648298","https://openalex.org/W2090156246","https://openalex.org/W2114351639","https://openalex.org/W2130042807","https://openalex.org/W2134840900","https://openalex.org/W2146712141","https://openalex.org/W2156973751","https://openalex.org/W2160844215","https://openalex.org/W2170558200","https://openalex.org/W2951478830","https://openalex.org/W2952834582","https://openalex.org/W3099994871","https://openalex.org/W3100344387"],"related_works":["https://openalex.org/W4213239787","https://openalex.org/W2045745654","https://openalex.org/W2114337652","https://openalex.org/W4388857216","https://openalex.org/W4377131110","https://openalex.org/W4294559962","https://openalex.org/W2046590706","https://openalex.org/W4390419005","https://openalex.org/W3013979739","https://openalex.org/W2949444602"],"abstract_inverted_index":{"The":[0,34,133,160,179],"aim":[1],"of":[2,44,54,84,101,123,130,139,155,165],"this":[3,85,124],"paper":[4],"is":[5,37,87,108,136,149,162,182,202],"to":[6,19,29,49,68,77,95,151],"show":[7,96],"that":[8,40,97,145,187],"spatial":[9,55],"coupling":[10],"can":[11,61],"be":[12],"viewed":[13],"not":[14],"only":[15],"as":[16,26,115],"a":[17,27,127,137,163],"means":[18],"build":[20],"better":[21,30],"graphical":[22,45],"models,":[23],"but":[24],"also":[25],"tool":[28],"understand":[31],"uncoupled":[32,79,117],"models.":[33],"starting":[35],"point":[36],"the":[38,52,64,73,78,98,102,106,110,140,146,152,156,166,169,176,183,188,193,197],"observation":[39,107],"some":[41],"asymptotic":[42],"properties":[43],"models":[46],"are":[47],"easier":[48],"prove":[50],"in":[51,196],"case":[53,76],"coupling.":[56],"In":[57],"such":[58],"cases,":[59],"one":[60,135],"then":[62],"use":[63,83,93],"so-called":[65,141],"interpolation":[66,94],"method":[67],"transfer":[69],"known":[70],"results":[71],"for":[72,88,112,116,126,192],"spatially":[74,113],"coupled":[75,114],"one.":[80],"Our":[81],"main":[82],"framework":[86],"LDPC":[89,131],"codes,":[90],"where":[91],"we":[92],"average":[99],"entropy":[100,195],"codeword":[103],"conditioned":[104],"on":[105],"asymptotically":[109],"same":[111],"ensembles.":[118,132],"We":[119],"give":[120],"three":[121],"applications":[122],"result":[125],"large":[128],"class":[129],"first":[134],"proof":[138,164],"Maxwell":[142],"construction":[143],"stating":[144],"MAP":[147,172,177],"threshold":[148,154],"equal":[150],"Area":[153],"BP":[157,170],"GEXIT":[158,173],"curve.":[159],"second":[161],"equality":[167],"between":[168],"and":[171],"curves":[174],"above":[175],"threshold.":[178],"third":[180],"application":[181],"intimately":[184],"related":[185],"fact":[186],"replica":[189],"symmetric":[190],"formula":[191],"conditional":[194],"infinite":[198],"block":[199],"length":[200],"limit":[201],"exact.":[203]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
