{"id":"https://openalex.org/W7213424423","doi":"https://doi.org/10.48550/arxiv.2609.16332","title":"Amortized Relaxed Locally Decodable Codes","display_name":"Amortized Relaxed Locally Decodable Codes","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213424423","doi":"https://doi.org/10.48550/arxiv.2609.16332"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16332","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16332","pdf_url":"https://arxiv.org/pdf/2609.16332","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.16332","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028278191","display_name":"Jeremiah Blocki","orcid":"https://orcid.org/0000-0002-5542-4674","observed_orcids":["https://orcid.org/0000-0002-5542-4674"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blocki, Jeremiah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021549646","display_name":"Justin Zhan","orcid":"https://orcid.org/0000-0001-8991-5669","observed_orcids":["https://orcid.org/0000-0001-8991-5669"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Justin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.006500000134110451,"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/T10237","display_name":"Cryptography and Data Security","score":0.00430000014603138,"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/error-tolerance","display_name":"error tolerance","score":0.7749999761581421},{"id":"https://openalex.org/keywords/rates","display_name":"rates","score":0.3919999897480011},{"id":"https://openalex.org/keywords/adversarial-channels","display_name":"adversarial channels","score":0.5370000004768372},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.503000020980835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6836000084877014},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6330000162124634},{"id":"https://openalex.org/C142417499","wikidata":"https://www.wikidata.org/wiki/Q331716","display_name":"Amortized analysis","level":3,"score":0.6262000203132629},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.5835999846458435},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5461999773979187},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.46790000796318054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4359000027179718},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4189999997615814},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.39160001277923584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37610000371932983},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.364300012588501},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.36250001192092896},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.334199994802475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3287000060081482},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.26829999685287476}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16332","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16332","pdf_url":"https://arxiv.org/pdf/2609.16332","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.16332","doi":"https://doi.org/10.48550/arxiv.2609.16332","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16332","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.16332","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16332","pdf_url":"https://arxiv.org/pdf/2609.16332","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213424423.pdf","grobid_xml":"https://content.openalex.org/works/W7213424423.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2786789903","https://openalex.org/W3156157822","https://openalex.org/W4296544078"],"related_works":["https://openalex.org/W4415367023","https://openalex.org/W3097401090","https://openalex.org/W7133629151","https://openalex.org/W6910371472","https://openalex.org/W7110064689","https://openalex.org/W7104041186","https://openalex.org/W4313227214","https://openalex.org/W2963950088","https://openalex.org/W7048553193","https://openalex.org/W2767436656"],"abstract_inverted_index":{"Locally":[0],"decodable":[1,64,130,161],"codes":[2,53,65],"(LDCs)":[3],"enable":[4],"recovery":[5],"of":[6,16,26,59,78,126,156,192,215],"any":[7,213],"message":[8,80,247],"symbol":[9,142,248],"by":[10],"probing":[11],"only":[12],"a":[13,19,84,127,139,236],"small":[14],"number":[15],"positions":[17],"in":[18,67,133],"possibly":[20],"corrupted":[21],"codeword.":[22],"The":[23],"central":[24],"parameters":[25,42],"an":[27,75,157],"LDC":[28],"are":[29],"its":[30],"rate,":[31,95,203,260],"locality,":[32,102],"and":[33,99,182,207,264],"error":[34,97,205,230,262],"tolerance.":[35],"Ideally,":[36],"one":[37],"would":[38],"like":[39],"all":[40],"three":[41],"to":[43],"be":[44],"constant.":[45],"However,":[46],"classical":[47],"lower":[48],"bounds":[49],"show":[50],"that":[51],"such":[52],"cannot":[54],"exist.":[55],"A":[56],"recent":[57],"line":[58],"work":[60,89],"introduced":[61],"amortized":[62,101,158,165,209,221],"locally":[63,129,160],"(aLDCs),":[66],"which":[68,134],"the":[69,112,118,124,135,154,168,193,198,229],"decoder":[70,136,219],"is":[71,123,179,228],"tasked":[72],"with":[73,93,167,201],"recovering":[74,235],"entire":[76],"block":[77,214,238],"consecutive":[79],"symbols":[81],"rather":[82,144],"than":[83,145,242],"single":[85],"symbol.":[86],"While":[87],"prior":[88,173],"obtained":[90],"ideal":[91,174],"aLDCs":[92],"constant":[94,96,100,202,204,208,259,261,265],"tolerance,":[98,206,263],"those":[103],"constructions":[104],"relied":[105],"on":[106],"either":[107],"shared":[108,187],"randomness":[109,188],"hidden":[110],"from":[111],"channel":[113],"or":[114,189],"computational":[115,190],"assumptions":[116,185],"restricting":[117],"channel.":[119,195],"Another":[120],"well-studied":[121],"relaxation":[122],"notion":[125,155],"relaxed":[128,159,169],"code":[131,162],"(RLDC),":[132],"may":[137],"output":[138],"special":[140],"failure":[141],"$\\bot$":[143],"risk":[146],"decoding":[147,166,170],"incorrectly.":[148],"In":[149],"this":[150],"work,":[151],"we":[152],"introduce":[153],"(aRLDC),":[163],"combining":[164],"paradigm.":[171],"Unlike":[172],"aLDC":[175],"constructions,":[176],"our":[177,218],"model":[178],"fully":[180],"information-theoretic":[181],"makes":[183],"no":[184,254],"about":[186],"limitations":[191],"adversarial":[194],"We":[196],"construct":[197],"first":[199],"aRLDC":[200],"locality.":[210,266],"Moreover,":[211],"for":[212],"length":[216],"$\u03a9(\\mathrm{polylog}(k))$,":[217],"achieves":[220],"locality":[222],"$1+\u03b4^{1":[223],"-":[224],"o(1)}$,":[225],"where":[226],"$\u03b4$":[227],"tolerance":[231],"parameter.":[232],"Thus,":[233],"asymptotically,":[234],"long":[237],"requires":[239],"essentially":[240],"less":[241],"two":[243],"codeword":[244],"probe":[245],"per":[246],"recovered.":[249],"By":[250],"contrast,":[251],"without":[252],"amortization":[253],"RLDC":[255],"can":[256],"simultaneously":[257],"achieve":[258]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-17T00:00:00"}