{"id":"https://openalex.org/W7153222389","doi":"https://doi.org/10.48550/arxiv.2604.07730","title":"The Asymmetric Hamming Bidistance and Distributions over Binary Asymmetric Channels","display_name":"The Asymmetric Hamming Bidistance and Distributions over Binary Asymmetric Channels","publication_year":2026,"publication_date":"2026-04-09","ids":{"openalex":"https://openalex.org/W7153222389","doi":"https://doi.org/10.48550/arxiv.2604.07730"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07730","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07730","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.07730","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132563581","display_name":"Shukai Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Shukai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120057946","display_name":"Cuiling Fan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan, Cuiling","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133380561","display_name":"Chunming Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Chunming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133339737","display_name":"Zhengchun Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Zhengchun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.3882000148296356,"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":0.3882000148296356,"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":0.3603000044822693,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.10260000079870224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6021999716758728},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.567799985408783},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.5600000023841858},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.546500027179718},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.506600022315979},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47510001063346863},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.4544000029563904},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.43230000138282776},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.3797999918460846}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6794999837875366},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6021999716758728},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.567799985408783},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.5600000023841858},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.546500027179718},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5267000198364258},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.506600022315979},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47510001063346863},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.4544000029563904},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4505999982357025},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.43230000138282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43140000104904175},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3797999918460846},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.3716000020503998},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.3668000102043152},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.3546000123023987},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.3393999934196472},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.3012999892234802},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.2946999967098236},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.2919999957084656},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.2793000042438507},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07730","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07730","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.07730","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07730","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7401414513587952}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"binary":[1,97],"asymmetric":[2,32],"channel":[3],"is":[4,107],"a":[5,51,87],"model":[6],"for":[7,15,60,96,136],"practical":[8],"communication":[9],"systems":[10],"where":[11],"the":[12,29,57,92,110,132,148],"error":[13,58,94],"probabilities":[14,59],"symbol":[16],"transitions":[17],"$0\\rightarrow":[18],"1$":[19],"and":[20,36,72,101,117,143,156],"$1\\rightarrow0$":[21],"differ":[22],"substantially.":[23],"In":[24],"this":[25,83],"paper,":[26],"we":[27,85,130],"introduce":[28],"notion":[30],"of":[31,55,139],"Hamming":[33],"bidistance":[34],"(AHB)":[35],"its":[37,128],"two-dimensional":[38],"distribution,":[39],"which":[40],"separately":[41],"captures":[42],"directional":[43],"discrepancies":[44],"between":[45],"codewords.":[46],"This":[47],"finer":[48],"characterization":[49],"enables":[50],"more":[52],"discriminative":[53],"analysis":[54],"decoding":[56,62],"maximum-likelihood":[61],"(MLD),":[63],"particularly":[64],"when":[65],"conventional":[66],"measures,":[67],"such":[68],"as":[69,160,162],"weight":[70],"distributions":[71,135],"existing":[73,112],"discrepancy-based":[74],"bounds,":[75],"fail":[76],"to":[77],"distinguish":[78],"code":[79],"performance.":[80],"Building":[81],"on":[82,91],"concept,":[84],"derive":[86],"new":[88],"upper":[89],"bound":[90],"average":[93],"probability":[95],"codes":[98,146,164],"under":[99],"MLD":[100],"show":[102],"that,":[103],"in":[104],"general,":[105],"it":[106],"incomparable":[108],"with":[109],"two":[111],"bounds":[113],"derived":[114],"by":[115],"Cotardo":[116],"Ravagnani":[118],"(IEEE":[119],"Trans.":[120],"Inf.":[121],"Theory,":[122],"68":[123],"(5),":[124],"2022).":[125],"To":[126],"demonstrate":[127],"applicability,":[129],"compute":[131],"complete":[133],"AHB":[134],"several":[137],"families":[138],"codes,":[140],"including":[141],"two-weight":[142],"three-weight":[144],"projective":[145],"(with":[147],"zero":[149],"codeword":[150],"removed)":[151],"via":[152],"strongly":[153],"regular":[154],"graphs":[155],"3-class":[157],"association":[158],"schemes,":[159],"well":[161],"nonlinear":[163],"constructed":[165],"from":[166],"symmetric":[167],"balanced":[168],"incomplete":[169],"block":[170],"designs":[171],"(SBIBDs).":[172]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-11T00:00:00"}