{"id":"https://openalex.org/W7214321771","doi":"https://doi.org/10.48550/arxiv.2609.29688","title":"Soft GRAND under Channel Uncertainty: Minimax Posterior-Envelope Ordering and Gallager-Exponent Preservation","display_name":"Soft GRAND under Channel Uncertainty: Minimax Posterior-Envelope Ordering and Gallager-Exponent Preservation","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7214321771","doi":"https://doi.org/10.48550/arxiv.2609.29688"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29688","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29688","pdf_url":"https://arxiv.org/pdf/2609.29688","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":"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/2609.29688","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034055082","display_name":"Behrooz Razeghi","orcid":"https://orcid.org/0000-0001-9568-4166","observed_orcids":["https://orcid.org/0000-0001-9568-4166"]},"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":true,"raw_author_name":"Razeghi, Behrooz","raw_affiliation_strings":["Harvard University , Cambridge , MA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University , Cambridge , MA , USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034055082"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9911999702453613,"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":0.9911999702453613,"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/T11130","display_name":"Coding theory and cryptography","score":0.0027000000700354576,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.0010999999940395355,"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/channel-uncertainty","display_name":"channel uncertainty","score":0.8799999952316284},{"id":"https://openalex.org/keywords/random-coding-exponent","display_name":"random coding exponent","score":0.7429999709129333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8514999747276306},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6236000061035156},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5375000238418579},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4837000072002411},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.47450000047683716},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.4278999865055084},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.42719998955726624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42309999465942383},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C32645036","wikidata":"https://www.wikidata.org/wiki/Q475164","display_name":"Stochastic ordering","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3034000098705292},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.2531999945640564},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29688","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29688","pdf_url":"https://arxiv.org/pdf/2609.29688","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.29688","doi":"https://doi.org/10.48550/arxiv.2609.29688","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29688","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29688","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29688","pdf_url":"https://arxiv.org/pdf/2609.29688","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2535218997","display_name":"Navigating Trust in Generative AI: An Information Theory and Optimal Transport Perspective","funder_award_id":"222339","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214321771.pdf","grobid_xml":"https://content.openalex.org/works/W7214321771.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W4406779549","https://openalex.org/W7134823362","https://openalex.org/W7134826158","https://openalex.org/W7166147825","https://openalex.org/W7166562584","https://openalex.org/W7171988397","https://openalex.org/W7197005410","https://openalex.org/W7203750973","https://openalex.org/W7204177565"],"related_works":["https://openalex.org/W7204177565","https://openalex.org/W4401693014","https://openalex.org/W2989652137","https://openalex.org/W2954103209","https://openalex.org/W4415368026","https://openalex.org/W4312314378","https://openalex.org/W2926325996","https://openalex.org/W7064533874","https://openalex.org/W2093186237","https://openalex.org/W4409310620"],"abstract_inverted_index":{"Soft":[0],"Guessing":[1],"Random":[2],"Additive":[3],"Noise":[4],"Decoding":[5],"queries":[6],"corrections":[7,20],"in":[8],"an":[9],"observation-dependent":[10],"order.":[11],"For":[12,63,93,119,226],"a":[13,50,69,124,143],"known":[14],"channel,":[15],"the":[16,40,44,55,78,82,105,112,115,134,147,155,173,194,205,209],"matched":[17,33,156,210],"order":[18,73,162,207],"ranks":[19,38],"by":[21,54,102,133],"nonincreasing":[22],"conditional":[23,151,175,181],"posterior":[24,66,91,170],"probability.":[25,92],"Under":[26,198],"channel":[27],"uncertainty,":[28],"admissible":[29,86],"channels":[30],"may":[31],"induce":[32],"orders":[34],"that":[35,140],"assign":[36],"different":[37],"to":[39],"same":[41,45],"correction":[42,61,117,126],"at":[43,75,215],"observation.":[46],"We":[47],"instead":[48],"use":[49],"posterior-envelope":[51,161],"order,":[52],"defined":[53],"pointwise":[56],"supremum":[57],"of":[58,81,114,136],"codebook-independent":[59],"uniform-input":[60,227,234],"posteriors.":[62],"fixed":[64,217],"measurable":[65,70],"representatives":[67],"and":[68,142,178,201,224],"envelope,":[71],"this":[72,96,164,230],"minimizes,":[74],"each":[76],"observation,":[77],"worst-case":[79],"logarithm":[80],"rank--posterior":[83],"product":[84,135],"over":[85],"channel--correction":[87],"pairs":[88,122],"with":[89,123],"positive":[90],"uniform-subset":[94,211],"codebooks,":[95],"finite-block":[97],"minimax":[98],"property":[99],"does":[100],"not":[101],"itself":[103],"determine":[104],"ensemble-average":[106,212],"error":[107,213],"exponent,":[108],"which":[109],"depends":[110],"on":[111,139,146,166,184],"distribution":[113,130],"realized":[116],"rank.":[118],"i.i.d.":[120],"correction--observation":[121],"finite":[125],"alphabet":[127,141],"whose":[128,187],"joint":[129],"is":[131],"dominated":[132],"counting":[137],"measure":[138,145],"$\u03c3$-finite":[144],"observation":[148,185],"space,":[149],"Arimoto":[150],"R\u00e9nyi":[152],"entropy":[153,202],"characterizes":[154],"rank-moment":[157],"spectrum.":[158],"An":[159],"auxiliary":[160,206],"preserves":[163],"spectrum":[165],"$[0,1]$":[167],"when":[168],"its":[169],"family":[171],"contains":[172],"corresponding":[174],"power":[176],"tilts":[177],"has":[179],"subexponential":[180],"Shtarkov":[182],"complexity":[183],"sets":[186],"complement":[188],"probabilities":[189],"decay":[190],"exponentially":[191],"faster":[192],"than":[193],"reciprocal":[195],"correction-space":[196],"cardinality.":[197],"additional":[199],"differentiability":[200],"nondegeneracy":[203],"conditions,":[204],"attains":[208],"exponent":[214,231],"every":[216],"normalized":[218],"code":[219],"rate":[220],"strictly":[221],"between":[222],"zero":[223],"one.":[225],"memoryless":[228],"channels,":[229],"equals":[232],"Gallager's":[233],"random-coding":[235],"exponent.":[236]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}
