{"id":"https://openalex.org/W2121189333","doi":"https://doi.org/10.1109/isit.2010.5513746","title":"Tight asymptotic bounds for the deletion channel with small deletion probabilities","display_name":"Tight asymptotic bounds for the deletion channel with small deletion probabilities","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2121189333","doi":"https://doi.org/10.1109/isit.2010.5513746","mag":"2121189333"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2010.5513746","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513746","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","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/A5086904495","display_name":"Adam Tauman Kalai","orcid":"https://orcid.org/0000-0002-4559-8574"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]},{"id":"https://openalex.org/I4400600948","display_name":"Microsoft Research New England (United States)","ror":"https://ror.org/010wkqn50","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Adam Kalai","raw_affiliation_strings":["Microsoft Research New England, UK","Microsoft Research, New England, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research New England, UK","institution_ids":["https://openalex.org/I4210164937"]},{"raw_affiliation_string":"Microsoft Research, New England, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062318856","display_name":"Michael Mitzenmacher","orcid":"https://orcid.org/0000-0001-5430-5457"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Mitzenmacher","raw_affiliation_strings":["School of Engineering and Applied Sciences, Harvard University, USA","[Harvard University, School of Engineering and Applied Sciences, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Sciences, Harvard University, USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"[Harvard University, School of Engineering and Applied Sciences, USA]","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101519422","display_name":"Madhu Sudan","orcid":"https://orcid.org/0000-0003-3718-6489"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]},{"id":"https://openalex.org/I4400600948","display_name":"Microsoft Research New England (United States)","ror":"https://ror.org/010wkqn50","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Madhu Sudan","raw_affiliation_strings":["Microsoft Research New England, UK","Microsoft Research, New England, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research New England, UK","institution_ids":["https://openalex.org/I4210164937"]},{"raw_affiliation_string":"Microsoft Research, New England, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I4400600948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.5226,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.99783768,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"997","last_page":"1001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9969000220298767,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7546212673187256},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.7519692182540894},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.670784592628479},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6291428804397583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.625878095626831},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6006191968917847},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5908209085464478},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.5476256608963013},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5202226042747498},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4298439621925354},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21894323825836182},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2113173007965088},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20270922780036926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09705513715744019},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08838954567909241},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07636120915412903}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7546212673187256},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.7519692182540894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.670784592628479},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6291428804397583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.625878095626831},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6006191968917847},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5908209085464478},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.5476256608963013},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5202226042747498},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4298439621925354},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21894323825836182},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2113173007965088},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20270922780036926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09705513715744019},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08838954567909241},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07636120915412903},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2010.5513746","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513746","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.330.6094","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.6094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.harvard.edu/~michaelm/postscripts/isit10submit.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"},{"id":"https://openalex.org/F4320336061","display_name":"Research England","ror":"https://ror.org/02wxr8x18"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1595409123","https://openalex.org/W2103188198","https://openalex.org/W2119486537","https://openalex.org/W2125870772","https://openalex.org/W2140017953","https://openalex.org/W2151069512","https://openalex.org/W2168917857","https://openalex.org/W2899702797","https://openalex.org/W2950808597","https://openalex.org/W4285719527","https://openalex.org/W6763943736"],"related_works":["https://openalex.org/W4243145179","https://openalex.org/W4255875982","https://openalex.org/W4244853958","https://openalex.org/W2029404707","https://openalex.org/W4285325679","https://openalex.org/W4247719608","https://openalex.org/W4237439661","https://openalex.org/W1928239295","https://openalex.org/W2743400891","https://openalex.org/W2167949116"],"abstract_inverted_index":{"In":[0],"this":[1,50],"paper,":[2],"we":[3],"consider":[4],"the":[5,9,14,18,34,43,57,68],"capacity":[6,35],"C":[7,37,64],"of":[8],"binary":[10,45],"deletion":[11,19],"channel":[12],"for":[13,29],"limiting":[15],"case":[16],"where":[17,40,67],"probability":[20],"p":[21,31,77],"goes":[22,78],"to":[23,73,79],"0.":[24,80],"It":[25],"is":[26,42,53,71],"known":[27],"that":[28,49,88],"any":[30],"<;":[32],"1/2,":[33],"satisfies":[36],"\u2265":[38],"1-H(p),":[39],"H":[41],"standard":[44],"entropy.":[46],"We":[47],"show":[48],"lower":[51],"bound":[52,63],"essentially":[54],"tight":[55],"in":[56,92],"limit,":[58],"by":[59],"providing":[60],"an":[61],"upper":[62],"\u2264":[65],"1-(1-o(1))H(p),":[66],"o(1)":[69],"term":[70],"understood":[72],"be":[74],"vanishing":[75],"as":[76],"Our":[81],"proof":[82],"utilizes":[83],"a":[84],"natural":[85],"counting":[86],"argument":[87],"should":[89],"prove":[90],"helpful":[91],"analyzing":[93],"related":[94],"channels.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
