{"id":"https://openalex.org/W2786732467","doi":"https://doi.org/10.1109/itw.2017.8277974","title":"Low-rate regular concatenated zigzag codes are capacity-approaching over the BEC","display_name":"Low-rate regular concatenated zigzag codes are capacity-approaching over the BEC","publication_year":2017,"publication_date":"2017-11-01","ids":{"openalex":"https://openalex.org/W2786732467","doi":"https://doi.org/10.1109/itw.2017.8277974","mag":"2786732467"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2017.8277974","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2017.8277974","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-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/A5100422467","display_name":"Haiyang Liu","orcid":"https://orcid.org/0000-0001-6567-8603"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210119392","display_name":"Institute of Microelectronics","ror":"https://ror.org/02s6gs133","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119392"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haiyang Liu","raw_affiliation_strings":["Institute of Microelectronics of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Microelectronics of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210119392","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100741314","display_name":"Li Ping","orcid":"https://orcid.org/0000-0002-4933-5093"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Li Ping","raw_affiliation_strings":["Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100422467"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210119392"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25179575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"111","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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":0.989300012588501,"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/T12029","display_name":"DNA and Biological Computing","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.7562039494514465},{"id":"https://openalex.org/keywords/zigzag","display_name":"Zigzag","score":0.7234031558036804},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.6261846423149109},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5862612724304199},{"id":"https://openalex.org/keywords/binary-erasure-channel","display_name":"Binary erasure channel","score":0.5798767805099487},{"id":"https://openalex.org/keywords/raptor-code","display_name":"Raptor code","score":0.5232160091400146},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5043376684188843},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.4970841705799103},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.4882640838623047},{"id":"https://openalex.org/keywords/serial-concatenated-convolutional-codes","display_name":"Serial concatenated convolutional codes","score":0.483963280916214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4590659439563751},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4323582649230957},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.42580458521842957},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.42212122678756714},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4005938768386841},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.3899625539779663},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38391509652137756},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3779201805591583},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.26132872700691223},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13747194409370422}],"concepts":[{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.7562039494514465},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.7234031558036804},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.6261846423149109},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5862612724304199},{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.5798767805099487},{"id":"https://openalex.org/C101252705","wikidata":"https://www.wikidata.org/wiki/Q7294373","display_name":"Raptor code","level":5,"score":0.5232160091400146},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5043376684188843},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.4970841705799103},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.4882640838623047},{"id":"https://openalex.org/C33529081","wikidata":"https://www.wikidata.org/wiki/Q18378194","display_name":"Serial concatenated convolutional codes","level":5,"score":0.483963280916214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4590659439563751},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4323582649230957},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.42580458521842957},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.42212122678756714},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4005938768386841},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.3899625539779663},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38391509652137756},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3779201805591583},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.26132872700691223},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13747194409370422},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw.2017.8277974","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2017.8277974","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1536930200","https://openalex.org/W1979023624","https://openalex.org/W1986354659","https://openalex.org/W2060945600","https://openalex.org/W2083406405","https://openalex.org/W2098917181","https://openalex.org/W2114468914","https://openalex.org/W2128765501","https://openalex.org/W2149490015","https://openalex.org/W2169732368","https://openalex.org/W2478708596","https://openalex.org/W2562965985","https://openalex.org/W2886691997","https://openalex.org/W4300188436","https://openalex.org/W6629343882","https://openalex.org/W6644924117"],"related_works":["https://openalex.org/W4245031194","https://openalex.org/W2296600582","https://openalex.org/W1983975287","https://openalex.org/W2363930252","https://openalex.org/W1985033232","https://openalex.org/W2543719358","https://openalex.org/W2343252454","https://openalex.org/W2964159840","https://openalex.org/W3084685600","https://openalex.org/W2135626675"],"abstract_inverted_index":{"Concatenated":[0],"zigzag":[1],"(CZ)":[2],"codes":[3,40,79,123,135],"have":[4],"been":[5],"widely":[6],"studied":[7],"for":[8,29,38,127],"practical":[9],"applications":[10],"due":[11],"to":[12,62,88,138],"their":[13],"low":[14],"encoding":[15],"complexity":[16],"and":[17,26,107],"excellent":[18],"performance.":[19],"However,":[20],"there":[21],"still":[22],"lacks":[23],"rigorous":[24],"analysis":[25,36],"optimization":[27],"techniques":[28],"CZ":[30,39,69,78,105,122],"codes.":[31],"This":[32,118],"paper":[33],"presents":[34],"an":[35],"technique":[37],"under":[41,71],"belief":[42],"propagation":[43],"(BP)":[44],"decoding":[45],"over":[46],"the":[47,64,85,89,96,99,108,114],"binary":[48],"erasure":[49],"channel":[50],"(BEC).":[51],"We":[52,74,92],"derive":[53],"a":[54,68,103],"pair":[55],"of":[56,67,102],"closed-form":[57],"density":[58],"evolution":[59],"(DE)":[60],"equations":[61],"characterize":[63],"asymptotic":[65],"behavior":[66],"code":[70,106],"BP":[72,100],"decoding.":[73],"show":[75],"that":[76,95,120],"capacity-approaching":[77],"can":[80],"be":[81],"designed":[82],"by":[83],"matching":[84],"curves":[86],"corresponding":[87,109],"DE":[90],"equations.":[91],"also":[93],"prove":[94],"gap":[97],"between":[98],"threshold":[101,111],"regular":[104,121],"Shannon":[110],"diminishes":[112],"when":[113],"rate":[115],"approaches":[116],"zero.":[117],"suggests":[119],"are":[124,136],"good":[125,132],"candidates":[126],"low-rate":[128],"communication":[129],"systems,":[130],"where":[131],"low-density":[133],"parity-check":[134],"difficult":[137],"construct.":[139]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}