{"id":"https://openalex.org/W4283815405","doi":"https://doi.org/10.1109/ncc55593.2022.9806780","title":"A Family of Capacity-Achieving Abelian Codes for the Binary Erasure Channel","display_name":"A Family of Capacity-Achieving Abelian Codes for the Binary Erasure Channel","publication_year":2022,"publication_date":"2022-05-24","ids":{"openalex":"https://openalex.org/W4283815405","doi":"https://doi.org/10.1109/ncc55593.2022.9806780"},"language":"en","primary_location":{"id":"doi:10.1109/ncc55593.2022.9806780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ncc55593.2022.9806780","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 National Conference on Communications (NCC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053548670","display_name":"Lakshmi Prasad Natarajan","orcid":"https://orcid.org/0000-0003-1552-5240"},"institutions":[{"id":"https://openalex.org/I65181880","display_name":"Indian Institute of Technology Hyderabad","ror":"https://ror.org/01j4v3x97","country_code":"IN","type":"education","lineage":["https://openalex.org/I65181880"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Lakshmi Prasad Natarajan","raw_affiliation_strings":["Indian Institute of Technology,Department of Electrical Engineering,Hyderabad, Sangareddy,India,502284"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology,Department of Electrical Engineering,Hyderabad, Sangareddy,India,502284","institution_ids":["https://openalex.org/I65181880"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001685956","display_name":"Prasad Krishnan","orcid":"https://orcid.org/0000-0001-9182-6278"},"institutions":[{"id":"https://openalex.org/I64189192","display_name":"International Institute of Information Technology, Hyderabad","ror":"https://ror.org/05f11g639","country_code":"IN","type":"education","lineage":["https://openalex.org/I64189192"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prasad Krishnan","raw_affiliation_strings":["Signal Processing and Communications Re-search Center, International Institute of Information Technology,Hyderabad,India,500032"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Signal Processing and Communications Re-search Center, International Institute of Information Technology,Hyderabad,India,500032","institution_ids":["https://openalex.org/I64189192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"abs 2110 14631","issue":null,"first_page":"425","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998000264167786,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9975000023841858,"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/binary-erasure-channel","display_name":"Binary erasure channel","score":0.6041843295097351},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5824265480041504},{"id":"https://openalex.org/keywords/erasure-code","display_name":"Erasure code","score":0.5659161806106567},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5521754026412964},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.550696074962616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5361165404319763},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.523804783821106},{"id":"https://openalex.org/keywords/erasure","display_name":"Erasure","score":0.5119408369064331},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.4966943860054016},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.49054187536239624},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4751417636871338},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44650155305862427},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.4370586574077606},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.42603451013565063},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.4104160964488983},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4096040427684784},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32608070969581604},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.3227936327457428},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.308239221572876},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29920336604118347},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27057117223739624},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.21995899081230164},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.10589581727981567},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05969157814979553}],"concepts":[{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.6041843295097351},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5824265480041504},{"id":"https://openalex.org/C137529215","wikidata":"https://www.wikidata.org/wiki/Q5385031","display_name":"Erasure code","level":3,"score":0.5659161806106567},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5521754026412964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.550696074962616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5361165404319763},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.523804783821106},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.5119408369064331},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.4966943860054016},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.49054187536239624},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4751417636871338},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44650155305862427},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.4370586574077606},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.42603451013565063},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.4104160964488983},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4096040427684784},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32608070969581604},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3227936327457428},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.308239221572876},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29920336604118347},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27057117223739624},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.21995899081230164},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.10589581727981567},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05969157814979553},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ncc55593.2022.9806780","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ncc55593.2022.9806780","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 National Conference on Communications (NCC)","raw_type":"proceedings-article"},{"id":"pmh:oai:raiith.iith.ac.in:10068","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400292","display_name":"Research Archive of Indian Institute of Technology Hyderabad (Indian Institute of Technology Hyderabad)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I65181880","host_organization_name":"Indian Institute of Technology Hyderabad","host_organization_lineage":["https://openalex.org/I65181880"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1975875771","https://openalex.org/W2039466900","https://openalex.org/W2041095358","https://openalex.org/W2053789337","https://openalex.org/W2170542295","https://openalex.org/W2204722887","https://openalex.org/W2282104735","https://openalex.org/W2540200239","https://openalex.org/W2542760130","https://openalex.org/W2591190829","https://openalex.org/W3208419198","https://openalex.org/W4210992409","https://openalex.org/W4289655172","https://openalex.org/W6803084894"],"related_works":["https://openalex.org/W1983975287","https://openalex.org/W1971149437","https://openalex.org/W2363930252","https://openalex.org/W1525070854","https://openalex.org/W2060392845","https://openalex.org/W2053950481","https://openalex.org/W2162141500","https://openalex.org/W2744779861","https://openalex.org/W2604463289","https://openalex.org/W4294811123"],"abstract_inverted_index":{"We":[0,81,106],"identify":[1,97],"a":[2,109,123],"large":[3],"family":[4,25,48,100,136],"of":[5,12,51,88,111,122,143,149],"abelian":[6,89],"codes":[7,22,50,90],"that":[8,56,117,133],"achieve":[9,43],"the":[10,13,40,119,129,147],"capacity":[11],"binary":[14],"erasure":[15],"channel":[16],"(BEC)":[17],"under":[18],"bit-MAP":[19],"decoding.":[20],"The":[21,140],"in":[23,128],"this":[24,134,144],"have":[26],"rich":[27],"automorphism":[28,104,120],"groups,":[29],"their":[30,74,103],"lengths":[31,55],"are":[32],"odd":[33,78],"integers,":[34],"and":[35,63,68,71,84,101,114,152],"they":[36],"can":[37],"asymptotically":[38],"(in":[39],"block":[41,54,79],"length)":[42],"any":[44,77],"code":[45,99,124,135],"rate.":[46],"This":[47],"contains":[49,73],"prime":[52],"power":[53],"were":[57],"originally":[58],"identified":[59],"by":[60,66],"Berman":[61],"(1967)":[62],"later":[64],"inves-tigated":[65],"Blackmore":[67],"Norton":[69],"(2001),":[70],"also":[72],"generalization":[75],"to":[76,96,125,131],"length.":[80],"use":[82,108],"Rajan":[83],"Siddiqi's":[85],"(1992)":[86],"characterization":[87],"using":[91],"discrete":[92],"Fourier":[93],"transform":[94],"(DFT)":[95],"our":[98],"study":[102],"groups.":[105],"then":[107],"result":[110],"Kumar,":[112],"Calderbank":[113],"Pfister":[115],"(2016)":[116],"relates":[118],"group":[121],"its":[126],"performance":[127],"BEC":[130,138],"show":[132],"achieves":[137],"capacity.":[139],"full":[141],"version":[142],"paper":[145],"including":[146],"proofs":[148],"all":[150],"claims":[151],"simulation":[153],"results":[154],"is":[155],"available":[156],"online":[157],"[1]":[158]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}