{"id":"https://openalex.org/W2964317445","doi":null,"title":"Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels","display_name":"Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2964317445","mag":"2964317445"},"language":"en","primary_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/121969","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/121969","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,"listed_in":[],"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":"http://purl.org/eprint/type/ConferencePaper"},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/1721.1/121969","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004351362","display_name":"Or Ordentlich","orcid":"https://orcid.org/0000-0002-5791-7923","observed_orcids":["https://orcid.org/0000-0002-5791-7923"]},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ordentlich, Or","raw_affiliation_strings":["University of Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031031216","display_name":"Yury Polyanskiy","orcid":"https://orcid.org/0000-0002-2109-0979","observed_orcids":["https://orcid.org/0000-0002-2109-0979"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Polyanskiy, Yury","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":16,"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":0.9775000214576721,"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":0.9775000214576721,"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":0.0210999995470047,"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":0.00019999999494757503,"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/reed-muller-codes","display_name":"Reed-Muller codes","score":0.9980000257492065},{"id":"https://openalex.org/keywords/binary-erasure-channel","display_name":"binary erasure channel","score":0.9190000295639038},{"id":"https://openalex.org/keywords/binary-symmetric-channel","display_name":"binary symmetric channel","score":1.0},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.6510000228881836},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"weight distribution","score":0.777999997138977},{"id":"https://openalex.org/keywords/capacity-achieving-codes","display_name":"capacity-achieving codes","score":0.7129999995231628}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6527804732322693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5819883346557617},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.34926870465278625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19260519742965698},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:dspace.mit.edu:1721.1/121969","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/121969","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,"listed_in":[],"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":"http://purl.org/eprint/type/ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/121969","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/121969","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,"listed_in":[],"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":"http://purl.org/eprint/type/ConferencePaper"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W568673721","https://openalex.org/W1549664537","https://openalex.org/W2071763320","https://openalex.org/W2266370294","https://openalex.org/W2591190829","https://openalex.org/W4245577611","https://openalex.org/W4302366875"],"related_works":["https://openalex.org/W6966473004","https://openalex.org/W301773371","https://openalex.org/W3049170756","https://openalex.org/W2266370294","https://openalex.org/W4385300855","https://openalex.org/W4415367526","https://openalex.org/W260895422","https://openalex.org/W4380679932","https://openalex.org/W2136391449","https://openalex.org/W4415064597"],"abstract_inverted_index":{"Consider":[0],"a":[1,174,181,186],"binary":[2,14,26],"linear":[3],"code":[4,123,175],"of":[5,53,78,82,99,121,146,155,163,192,198],"length":[6],"N,":[7],"minimum":[8,70,119],"distance":[9,71,120],"d-{\\min},":[10],"transmission":[11],"over":[12],"the":[13,25,50,54,69,76,79,96,100,102,118,122,137,153,156,161,164,190,193,196,203],"erasure":[15],"channel":[16,28],"with":[17,29],"parameter":[18,30],"0":[19,31,67],"<":[20,22,32,34],"\\epsilon":[21,33],"1":[23],"or":[24,178],"symmetric":[27],"\\frac{1}{2},":[35],"and":[36,44],"block-MAP":[37,55],"decoding.":[38],"It":[39],"was":[40],"shown":[41],"by":[42,89],"Tillich":[43],"Zemor":[45],"that":[46,91,152],"in":[47],"this":[48,87,167],"case":[49],"error":[51],"probability":[52],"decoder":[56],"transitions":[57],"'quickly'":[58],"from":[59],"\\delta":[60,65],"to":[61,131],"1-\\delta":[62],"for":[63,111,141],"any":[64,112,142],">":[66,114],"if":[68,117],"is":[72,81,124,136,176,200],"large.":[73],"In":[74],"particular":[75],"width":[77,104,154],"transition":[80,103,139,157],"order":[83],"O(1/\\sqrt{d-{\\min}}).":[84],"We":[85,150],"strengthen":[86],"result":[88,168],"showing":[90],"under":[92],"suitable":[93],"conditions":[94],"on":[95,172,189,202],"weight":[97],"distribution":[98],"code,":[101,143],"can":[105],"be":[106],"as":[107,109],"small":[108],"\\Theta(1/N^{\\frac{1}{2}-\\kappa}),":[110],"\\kappa":[113],"0,":[115],"even":[116],"not":[125],"linear.":[126],"This":[127],"condition":[128],"applies":[129],"e.g.,":[130],"Reed-Mueller":[132],"codes.":[133],"Since":[134],"\\Theta(1/N^{\\frac{1}{2}})":[135],"smallest":[138],"possible":[140],"we":[144,184],"speak":[145],"'almost'":[147],"optimal":[148],"scaling.":[149],"emphasize":[151],"says":[158],"nothing":[159],"about":[160],"location":[162],"transition.":[165],"Therefore":[166],"has":[169],"no":[170],"bearing":[171],"whether":[173],"capacity-achieving":[177],"not.":[179],"As":[180],"second":[182],"contribution,":[183],"present":[185],"new":[187],"estimate":[188],"derivative":[191],"EXIT":[194],"function,":[195],"proof":[197],"which":[199],"based":[201],"Blowing-Up":[204],"Lemma.":[205]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2019-07-30T00:00:00"}