{"id":"https://openalex.org/W2900073520","doi":"https://doi.org/10.1109/tit.2019.2935772","title":"Broadcasting on Random Directed Acyclic Graphs","display_name":"Broadcasting on Random Directed Acyclic Graphs","publication_year":2019,"publication_date":"2019-08-16","ids":{"openalex":"https://openalex.org/W2900073520","doi":"https://doi.org/10.1109/tit.2019.2935772","mag":"2900073520"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2935772","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2935772","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/1811.03946","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073197040","display_name":"Anuran Makur","orcid":"https://orcid.org/0000-0002-2978-8116"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Anuran Makur","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, USA"],"raw_orcid":"https://orcid.org/0000-0002-2978-8116","affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013467728","display_name":"Elchanan Mossel","orcid":"https://orcid.org/0000-0001-7812-7886"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Elchanan Mossel","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031031216","display_name":"Yury Polyanskiy","orcid":null},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Yury Polyanskiy","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, USA"],"raw_orcid":"https://orcid.org/0000-0002-2109-0979","affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.5593,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.84113955,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"66","issue":"2","first_page":"780","last_page":"812"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9973000288009644,"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":0.9973000288009644,"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/T12029","display_name":"DNA and Biological Computing","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.6569209694862366},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5791975259780884},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5769526362419128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5419240593910217},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49677616357803345},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.49203917384147644},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48311328887939453},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.45064905285835266},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4361754357814789},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.4301583468914032},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33370721340179443},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2682725787162781}],"concepts":[{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.6569209694862366},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5791975259780884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5769526362419128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5419240593910217},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49677616357803345},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.49203917384147644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48311328887939453},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.45064905285835266},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4361754357814789},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.4301583468914032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33370721340179443},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2682725787162781},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2019.2935772","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2935772","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:1811.03946","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.03946","pdf_url":"https://arxiv.org/pdf/1811.03946","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"},{"id":"pmh:oai:dspace.mit.edu:1721.1/136548","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/136548","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.03946","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.03946","pdf_url":"https://arxiv.org/pdf/1811.03946","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/G1049432417","display_name":null,"funder_award_id":"ITS/066/17FP","funder_id":"https://openalex.org/F4320326427","funder_display_name":"Innovation and Technology Fund"},{"id":"https://openalex.org/G2641300687","display_name":null,"funder_award_id":"CCF-09-39370","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4910389545","display_name":null,"funder_award_id":"N00014-17-1-2598","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4956351018","display_name":null,"funder_award_id":"DMS-1737944","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6675008928","display_name":null,"funder_award_id":"CCF-12-53205","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8072263602","display_name":null,"funder_award_id":"CCF-1665252","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"},{"id":"https://openalex.org/F4320326427","display_name":"Innovation and Technology Fund","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":76,"referenced_works":["https://openalex.org/W26421094","https://openalex.org/W54567006","https://openalex.org/W116481949","https://openalex.org/W121824094","https://openalex.org/W139685425","https://openalex.org/W390146837","https://openalex.org/W998121262","https://openalex.org/W1507653385","https://openalex.org/W1511368807","https://openalex.org/W1818081266","https://openalex.org/W1846857138","https://openalex.org/W1981663184","https://openalex.org/W1982172875","https://openalex.org/W1986083251","https://openalex.org/W1988928480","https://openalex.org/W1993590277","https://openalex.org/W1994823074","https://openalex.org/W1994908596","https://openalex.org/W1996199671","https://openalex.org/W2000315374","https://openalex.org/W2019059781","https://openalex.org/W2024231387","https://openalex.org/W2029127025","https://openalex.org/W2036744511","https://openalex.org/W2039494655","https://openalex.org/W2042790585","https://openalex.org/W2043509032","https://openalex.org/W2054104481","https://openalex.org/W2055309977","https://openalex.org/W2064369971","https://openalex.org/W2075008459","https://openalex.org/W2089146215","https://openalex.org/W2097415784","https://openalex.org/W2102902005","https://openalex.org/W2103012681","https://openalex.org/W2112400707","https://openalex.org/W2126216439","https://openalex.org/W2128020980","https://openalex.org/W2129774678","https://openalex.org/W2137906383","https://openalex.org/W2141432878","https://openalex.org/W2148180254","https://openalex.org/W2148533576","https://openalex.org/W2160892640","https://openalex.org/W2163994692","https://openalex.org/W2164716567","https://openalex.org/W2165469059","https://openalex.org/W2168290833","https://openalex.org/W2290247654","https://openalex.org/W2293231900","https://openalex.org/W2471517265","https://openalex.org/W2497735908","https://openalex.org/W2559839022","https://openalex.org/W2595897327","https://openalex.org/W2751862591","https://openalex.org/W2753908209","https://openalex.org/W2765846489","https://openalex.org/W2894544709","https://openalex.org/W2897569278","https://openalex.org/W2950361113","https://openalex.org/W2963060561","https://openalex.org/W2963923339","https://openalex.org/W2976643397","https://openalex.org/W3017482587","https://openalex.org/W3102586875","https://openalex.org/W3105479371","https://openalex.org/W3182208082","https://openalex.org/W4230410498","https://openalex.org/W4230606898","https://openalex.org/W4233413206","https://openalex.org/W4234100157","https://openalex.org/W4238472918","https://openalex.org/W4243718192","https://openalex.org/W4254268221","https://openalex.org/W4301441647","https://openalex.org/W6755116403"],"related_works":["https://openalex.org/W2146569528","https://openalex.org/W4287028074","https://openalex.org/W2106828717","https://openalex.org/W3191289342","https://openalex.org/W1998712144","https://openalex.org/W4300165677","https://openalex.org/W3164774158","https://openalex.org/W4297817344","https://openalex.org/W2372211403","https://openalex.org/W1498463151"],"abstract_inverted_index":{"We":[0,241],"study":[1],"the":[2,6,27,38,54,76,115,118,128,141,175,191,224,237,255,268,310],"following":[3],"generalization":[4],"of":[5,9,29,134,143,159,177,215,300,314],"wellknown":[7],"model":[8],"broadcasting":[10,186,364],"on":[11],"trees.":[12],"Consider":[13],"an":[14,147],"infinite":[15],"directed":[16],"acyclic":[17],"graph":[18],"(DAG)":[19],"with":[20,91,132,213,295,359],"a":[21,59,106,198,233,244,274,334,339],"unique":[22],"source":[23,55],"vertex":[24,45,56,68,99],"X.":[25],"Let":[26],"collection":[28],"vertices":[30,145],"at":[31,117,146],"distance":[32],"k":[33,64],"from":[34,72,138],"X":[35,131],"be":[36,124,318,366],"called":[37],"kth":[39],"layer,":[40,78],"and":[41,162,164,201,210,218,298],"suppose":[42],"every":[43],"non-source":[44],"has":[46],"indegree":[47],"d":[48,70,102,207,228,250,349],"\u2265":[49,65,208,251],"2.":[50],"At":[51,62],"layer":[52,63,150,353],"0,":[53],"is":[57,122,154,187,196,270],"given":[58],"random":[60,211],"bit.":[61],"1,":[66],"each":[67],"receives":[69],"bits":[71],"its":[73,101],"parents":[74],"in":[75,167,320,329,341,361],"(k-1)th":[77],"which":[79,182],"are":[80,85,258],"transmitted":[81],"along":[82],"edges":[83],"that":[84,113,185,254,309],"independent":[86],"binary":[87],"symmetric":[88],"channels":[89],"(BSCs)":[90],"crossover":[92],"probability":[93,133],"\u03b4":[94,195],"\u2208":[95],"(0,":[96],"1/2).":[97],"Each":[98],"combines":[100],"noisy":[103],"inputs":[104],"using":[105,140,273],"2":[107],"deterministic":[108,322],"d-ary":[109],"Boolean":[110],"processing":[111,220,239,265],"function":[112,202],"generates":[114],"value":[116],"vertex.":[119],"The":[120],"goal":[121],"to":[123,126,157,260,272,346,356,365],"able":[125],"reconstruct":[127],"original":[129],"bit":[130,340],"error":[135],"bounded":[136,296,342],"away":[137],"1/2":[139],"values":[142],"all":[144],"arbitrarily":[148],"deep":[149],"k.":[151],"This":[152],"question":[153],"closely":[155],"related":[156],"models":[158],"reliable":[160],"computation":[161],"storage,":[163],"information":[165],"flow":[166],"biological":[168],"networks.":[169],"In":[170,305],"this":[171],"paper,":[172],"we":[173,183,222,231,285,307],"treat":[174],"case":[176],"randomly":[178],"constructed":[179],"DAGs,":[180],"for":[181,236,248,279,337,363],"show":[184,308],"only":[188],"possible":[189],"if":[190,267],"BSC":[192,281],"noise":[193,282],"level":[194,283],"below":[197],"certain":[199],"(degree":[200],"dependent)":[203],"critical":[204,225],"threshold.":[205,226],"For":[206,227],"3,":[209],"DAGs":[212,288,316,344],"layers":[214,299,313],"size":[216,301],"\u03a9(log(k))":[217],"majority":[219],"functions,":[221],"identify":[223],"=":[229,350],"2,":[230],"establish":[232],"similar":[234],"result":[235,247],"NAND":[238],"function.":[240],"also":[242],"prove":[243],"partial":[245],"converse":[246],"odd":[249],"3":[252],"illustrating":[253],"identified":[256],"thresholds":[257],"impossible":[259],"improve":[261],"by":[262],"selecting":[263],"different":[264],"functions":[266],"decoder":[269],"restricted":[271],"single":[275],"vertex's":[276],"value.":[277],"Finally,":[278],"any":[280],"\u03b4,":[284],"construct":[286],"explicit":[287],"(using":[289],"regular":[290],"bipartite":[291],"lossless":[292],"expander":[293],"graphs)":[294],"degree":[297,343],"\u0398(log(k))":[302],"admitting":[303],"reconstruction.":[304],"particular,":[306],"first":[311],"r":[312],"such":[315],"can":[317],"generated":[319],"either":[321],"quasipolynomial":[323],"time":[324,328],"or":[325],"randomized":[326],"polylogarithmic":[327],"r.":[330],"These":[331],"results":[332],"portray":[333],"doubly-exponential":[335],"advantage":[336],"storing":[338],"compared":[345],"trees,":[347],"where":[348],"1":[351],"but":[352],"sizes":[354],"need":[355],"grow":[357],"exponentially":[358],"depth":[360],"order":[362],"possible.":[367]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}