{"id":"https://openalex.org/W1498822354","doi":"https://doi.org/10.1109/tit.2015.2496308","title":"The Random Coding Bound Is Tight for the Average Linear Code or Lattice","display_name":"The Random Coding Bound Is Tight for the Average Linear Code or Lattice","publication_year":2015,"publication_date":"2015-10-30","ids":{"openalex":"https://openalex.org/W1498822354","doi":"https://doi.org/10.1109/tit.2015.2496308","mag":"1498822354"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2496308","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2496308","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1307.5524","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060478990","display_name":"Yuval Domb","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yuval Domb","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027550575","display_name":"Ram Zamir","orcid":"https://orcid.org/0000-0003-1800-3886"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ram Zamir","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066905280","display_name":"Meir Feder","orcid":"https://orcid.org/0000-0002-1290-0482"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Meir Feder","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060478990"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01724263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"62","issue":"1","first_page":"121","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/exponent","display_name":"Exponent","score":0.7155619859695435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6362103223800659},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6350195407867432},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5526109337806702},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5007357597351074},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4448424279689789},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.43237465620040894},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4267190992832184},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.42076438665390015},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4166313707828522},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21905171871185303},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18145829439163208},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13848578929901123},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.052624404430389404}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7155619859695435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6362103223800659},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6350195407867432},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5526109337806702},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5007357597351074},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4448424279689789},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.43237465620040894},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4267190992832184},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.42076438665390015},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4166313707828522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21905171871185303},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18145829439163208},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13848578929901123},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.052624404430389404},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2015.2496308","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2496308","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:1307.5524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.5524","pdf_url":"https://arxiv.org/pdf/1307.5524","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":"","raw_type":"text"},{"id":"mag:1498822354","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1307.5524","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.744.1431","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.744.1431","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/1307.5524.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1307.5524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1307.5524","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1307.5524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.5524","pdf_url":"https://arxiv.org/pdf/1307.5524","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1537675645","https://openalex.org/W2015850986","https://openalex.org/W2085581636","https://openalex.org/W2092271237","https://openalex.org/W2096667287","https://openalex.org/W2099792872","https://openalex.org/W2142901448","https://openalex.org/W2151450116","https://openalex.org/W2154147983","https://openalex.org/W2160973043","https://openalex.org/W2324303215","https://openalex.org/W2950754480","https://openalex.org/W4237963784","https://openalex.org/W4292414116"],"related_works":["https://openalex.org/W2963962111","https://openalex.org/W2054729364","https://openalex.org/W1537675645","https://openalex.org/W2949246484","https://openalex.org/W3104263091","https://openalex.org/W2563994828","https://openalex.org/W2038672318","https://openalex.org/W2085581636","https://openalex.org/W2904372851","https://openalex.org/W2747324282","https://openalex.org/W2762400634","https://openalex.org/W1969693636","https://openalex.org/W1963764453","https://openalex.org/W3132309254","https://openalex.org/W3198110814","https://openalex.org/W2886676188","https://openalex.org/W3102287958","https://openalex.org/W2803095839","https://openalex.org/W2952645742","https://openalex.org/W1653591572"],"abstract_inverted_index":{"In":[0],"1973,":[1],"Gallager":[2],"proved":[3,69],"that":[4,25,53,77],"the":[5,12,26,32,37,40,45],"random-coding":[6,27,83],"bound":[7],"is":[8,68,75],"exponentially":[9],"tight":[10],"for":[11,59,85],"random":[13,41,61,87],"code":[14],"ensemble":[15,62,88],"at":[16],"all":[17],"rates,":[18],"even":[19],"below":[20],"expurgation.":[21],"This":[22,66],"result":[23],"explained":[24],"exponent":[28,34,84],"does":[29],"not":[30],"achieve":[31],"expurgation":[33],"due":[35],"to":[36,81],"properties":[38],"of":[39,44,63,89],"ensemble,":[42],"irrespective":[43],"utilized":[46],"bounding":[47],"technique.":[48],"It":[49],"has":[50],"been":[51],"conjectured":[52],"this":[54,71,78],"same":[55],"behavior":[56],"holds":[57],"true":[58],"a":[60,86],"linear":[64],"codes.":[65],"conjecture":[67],"in":[70],"paper.":[72],"Additionally,":[73],"it":[74],"shown":[76],"property":[79],"extends":[80],"Poltyrev's":[82],"lattices.":[90]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
