{"id":"https://openalex.org/W2766124948","doi":"https://doi.org/10.1109/lcomm.2017.2767028","title":"Tight Lower and Upper Bounds on the Minimum Distance of LDPC Codes","display_name":"Tight Lower and Upper Bounds on the Minimum Distance of LDPC Codes","publication_year":2017,"publication_date":"2017-11-01","ids":{"openalex":"https://openalex.org/W2766124948","doi":"https://doi.org/10.1109/lcomm.2017.2767028","mag":"2766124948"},"language":"en","primary_location":{"id":"doi:10.1109/lcomm.2017.2767028","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcomm.2017.2767028","pdf_url":null,"source":{"id":"https://openalex.org/S147316732","display_name":"IEEE Communications Letters","issn_l":"1089-7798","issn":["1089-7798","1558-2558","2373-7891"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications Letters","raw_type":"journal-article"},"type":"article","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/A5080145492","display_name":"Yoones Hashemi","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yoones Hashemi","raw_affiliation_strings":["Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046274917","display_name":"Amir H. Banihashemi","orcid":"https://orcid.org/0000-0003-0685-5256"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Amir H. Banihashemi","raw_affiliation_strings":["Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080145492"],"corresponding_institution_ids":["https://openalex.org/I67031392"],"apc_list":null,"apc_paid":null,"fwci":2.072,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.89059963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"1","first_page":"33","last_page":"36"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9926999807357788,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.98580002784729,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6394087076187134},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5611464381217957},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4919154644012451},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4594815969467163},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42721307277679443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35664358735084534},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3539941608905792},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11076146364212036}],"concepts":[{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6394087076187134},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5611464381217957},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4919154644012451},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4594815969467163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42721307277679443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35664358735084534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3539941608905792},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11076146364212036},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcomm.2017.2767028","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcomm.2017.2767028","pdf_url":null,"source":{"id":"https://openalex.org/S147316732","display_name":"IEEE Communications Letters","issn_l":"1089-7798","issn":["1089-7798","1558-2558","2373-7891"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7921809464","display_name":null,"funder_award_id":"217239-2013-RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1976450468","https://openalex.org/W2071304218","https://openalex.org/W2076838340","https://openalex.org/W2110841034","https://openalex.org/W2119990840","https://openalex.org/W2130332106","https://openalex.org/W2133068391","https://openalex.org/W2521520100","https://openalex.org/W2531628009","https://openalex.org/W2558776151","https://openalex.org/W2579410364","https://openalex.org/W2619905542","https://openalex.org/W4237031056","https://openalex.org/W6732059664"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2980963558","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542"],"abstract_inverted_index":{"In":[0],"this":[1],"letter,":[2],"we":[3,119,151],"obtain":[4,121],"lower":[5,91,134,210,237],"and":[6,41,195,199,203,211,215],"upper":[7,149,180,212,239],"bounds":[8,23,213],"on":[9,97,141,182],"the":[10,28,66,98,106,127,133,148,164,201,219,244,250],"minimum":[11],"distance":[12],"d":[13,142,183,223,229],"<sub":[14,82,94,110,115,138,143,184,224,230],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,83,95,111,116,139,144,185,225,231],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">min</sub>":[16,145,186,226,232],"of":[17,32,39,70,100,136,160,166,193,205,243,249,252],"low-density":[18],"parity-check":[19],"(LDPC)":[20],"codes.":[21],"The":[22,43],"are":[24,247],"derived":[25],"by":[26],"categorizing":[27],"non-zero":[29],"code":[30,35,47,68,73,102,124],"words":[31,48,69],"an":[33,59,71,122,179],"LDPC":[34,72,197],"into":[36],"two":[37],"categories":[38],"elementary":[40,67,123,158],"non-elementary.":[42],"first":[44],"category":[45],"contains":[46],"whose":[49],"induced":[50],"subgraph":[51],"has":[52],"only":[53],"degree-2":[54],"check":[55],"nodes.":[56],"We":[57,87,188],"propose":[58],"efficient":[60],"search":[61,107,154],"algorithm":[62,155],"that":[63],"can":[64],"find":[65],"with":[74,108,126],"weight":[75,99,129,176],"less":[76],"than":[77],"a":[78,81,90,109,171,190],"certain":[79],"value":[80,221],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">max</sub>":[84,112],",":[85,118,233],"exhaustively.":[86],"also":[88],"derive":[89],"bound":[92,135,181],"L":[93,114,137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">ne</sub>":[96,117,140],"non-elementary":[101],"words.":[103],"By":[104],"performing":[105],"=":[113],"either":[120],"word":[125],"smallest":[128],"dmin,":[130],"or":[131,234,238],"establish":[132],".":[146,187,227],"For":[147],"bound,":[150],"modify":[152],"our":[153,206],"to":[156],"reach":[157,251],"codewords":[159],"larger":[161],"weights":[162],"at":[163],"cost":[165],"being":[167],"non-exhaustive.":[168],"Once":[169],"such":[170],"codeword":[172],"is":[173],"found,":[174],"its":[175],"acts":[177],"as":[178],"examine":[189],"large":[191],"number":[192],"regular":[194],"irregular":[196],"codes,":[198],"demonstrate":[200],"efficiency":[202],"versatility":[204],"technique":[207],"in":[208,216],"finding":[209],"on,":[214],"many":[217,242],"cases":[218],"exact":[220],"of,":[222],"Finding":[228],"establishing":[235],"search-based":[236],"bounds,":[240],"for":[241],"examined":[245],"codes":[246],"out":[248],"any":[253],"existing":[254],"algorithm.":[255]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
