{"id":"https://openalex.org/W2912975485","doi":"https://doi.org/10.1109/isit.2019.8849509","title":"A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel","display_name":"A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2912975485","doi":"https://doi.org/10.1109/isit.2019.8849509","mag":"2912975485"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849509","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.06975","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012790875","display_name":"Enrico Paolini","orcid":"https://orcid.org/0000-0003-0781-531X"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Enrico Paolini","raw_affiliation_strings":["DEI, University of Bologna, Cesena (FC), Italy","University of Bologna"],"affiliations":[{"raw_affiliation_string":"DEI, University of Bologna, Cesena (FC), Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"University of Bologna","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023681550","display_name":"Gianluigi Liva","orcid":"https://orcid.org/0000-0001-8657-2963"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gianluigi Liva","raw_affiliation_strings":["KN-SAN, German Aerospace Center, Wessling, Germany","[German Aerospace Center]"],"affiliations":[{"raw_affiliation_string":"KN-SAN, German Aerospace Center, Wessling, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"[German Aerospace Center]","institution_ids":["https://openalex.org/I2898391981"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012790875"],"corresponding_institution_ids":["https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01597487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1732","last_page":"1736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":1.0,"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":1.0,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9987000226974487,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9984999895095825,"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/erasure","display_name":"Erasure","score":0.8008794784545898},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.7280632257461548},{"id":"https://openalex.org/keywords/binary-erasure-channel","display_name":"Binary erasure channel","score":0.6933115720748901},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6747334003448486},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.6173157095909119},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6131788492202759},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5669590830802917},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5059863924980164},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.45880237221717834},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44751572608947754},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4052997827529907},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39943867921829224},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37723615765571594},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2796472907066345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26166003942489624},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.21377652883529663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08219254016876221}],"concepts":[{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.8008794784545898},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7280632257461548},{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.6933115720748901},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6747334003448486},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.6173157095909119},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6131788492202759},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5669590830802917},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5059863924980164},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.45880237221717834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44751572608947754},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4052997827529907},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39943867921829224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37723615765571594},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2796472907066345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26166003942489624},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.21377652883529663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08219254016876221},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/isit.2019.8849509","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1901.06975","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.06975","pdf_url":"https://arxiv.org/pdf/1901.06975","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":"mag:2912975485","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1901.06975.pdf","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:cris.unibo.it:11585/722442","is_oa":false,"landing_page_url":"https://ieeexplore.ieee.org/document/8849509","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"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":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:elib.dlr.de:131885","is_oa":false,"landing_page_url":"https://elib.dlr.de/131885/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196266","display_name":"elib (German Aerospace Center)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2898391981","host_organization_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","host_organization_lineage":["https://openalex.org/I2898391981"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Konferenzbeitrag"},{"id":"doi:10.48550/arxiv.1901.06975","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1901.06975","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:1901.06975","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.06975","pdf_url":"https://arxiv.org/pdf/1901.06975","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":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2912975485.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2019119407","https://openalex.org/W2095882513","https://openalex.org/W2097415784","https://openalex.org/W2114449874","https://openalex.org/W2128392432","https://openalex.org/W2128765501","https://openalex.org/W2142901448","https://openalex.org/W2157587788","https://openalex.org/W2163496715","https://openalex.org/W2296600582","https://openalex.org/W2963072837","https://openalex.org/W2975088794","https://openalex.org/W4229922087","https://openalex.org/W4300188436"],"related_works":["https://openalex.org/W2975088794","https://openalex.org/W3157123936","https://openalex.org/W2169154778","https://openalex.org/W2086113376","https://openalex.org/W3138306355","https://openalex.org/W1969693636","https://openalex.org/W2114449874","https://openalex.org/W2383587702","https://openalex.org/W2112155927","https://openalex.org/W1537675645","https://openalex.org/W2085581636","https://openalex.org/W2963024103","https://openalex.org/W1972831370","https://openalex.org/W2566803863","https://openalex.org/W2152744672","https://openalex.org/W1621877253","https://openalex.org/W1780477715","https://openalex.org/W2137667444","https://openalex.org/W3214311941","https://openalex.org/W2962859014"],"abstract_inverted_index":{"A":[0],"lower":[1,23,62,101],"bound":[2,24,63,102],"on":[3,16,107],"the":[4,17,37,49,64,88,97,103,108],"maximum":[5],"likelihood":[6],"(ML)":[7],"decoding":[8,67,105],"error":[9],"exponent":[10],"of":[11,33,119],"linear":[12,74,83],"block":[13],"code":[14],"ensembles,":[15],"erasure":[18,34,109],"channel,":[19],"is":[20,94],"developed.":[21],"The":[22],"turns":[25],"to":[26,44,54],"be":[27],"positive,":[28],"over":[29],"an":[30],"ensemble-specific":[31],"interval":[32],"probabilities,":[35],"when":[36],"ensemble":[38],"weight":[39,52],"spectral":[40],"shape":[41],"function":[42],"tends":[43,53],"a":[45,90,114],"negative":[46],"value":[47],"as":[48],"fractional":[50],"codeword":[51],"zero.":[55],"For":[56],"these":[57],"ensembles":[58],"we":[59,99],"can":[60,100],"therefore":[61],"block-wise":[65],"ML":[66,104],"threshold.":[68],"Two":[69],"examples":[70],"are":[71],"presented,":[72],"namely,":[73],"random":[75,84],"parity-check":[76],"codes":[77,81],"and":[78],"fixed-rate":[79],"Raptor":[80],"with":[82],"precoders.":[85],"While":[86],"for":[87,96],"former":[89],"full":[91],"analytical":[92],"solution":[93],"possible,":[95],"latter":[98],"threshold":[106],"channel":[110],"by":[111],"simply":[112],"solving":[113],"2":[115,117],"\u00d7":[116],"system":[118],"nonlinear":[120],"equations.":[121]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}