<> <http://www.w3.org/2000/01/rdf-schema#comment> "The repository administrator has not yet configured an RDF license."^^<http://www.w3.org/2001/XMLSchema#string> .
<> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10152229> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/title> "How to send a real number using a single bit (and some shared randomness)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/ontology/bibo/abstract> "We consider the fundamental problem of communicating an estimate of a real number x ∈ [0,1] using a single bit. A sender that knows x chooses a value X ∈ {0,1} to transmit. In turn, a receiver estimates x based on the value of X. The goal is to minimize the cost, defined as the worst-case (over the choice of x) expected squared error.\r\nWe first overview common biased and unbiased estimation approaches and prove their optimality when no shared randomness is allowed. We then show how a small amount of shared randomness, which can be as low as a single bit, reduces the cost in both cases. Specifically, we derive lower bounds on the cost attainable by any algorithm with unrestricted use of shared randomness and propose optimal and near-optimal solutions that use a small number of shared random bits. Finally, we discuss open problems and future directions."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/date> "2021" .
<https://discovery.ucl.ac.uk/id/document/1474780> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> .
<https://discovery.ucl.ac.uk/id/org/ext-f649eb193dc1dc3a20f7a4c7c4ece045> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Organization> .
<https://discovery.ucl.ac.uk/id/org/ext-f649eb193dc1dc3a20f7a4c7c4ece045> <http://xmlns.com/foaf/0.1/name> "Schloss Dagstuhl - Leibniz-Zentrum für Informatik"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/publisher> <https://discovery.ucl.ac.uk/id/org/ext-f649eb193dc1dc3a20f7a4c7c4ece045> .
<https://discovery.ucl.ac.uk/id/publication/ext-0b12c6835e67c7b73d5c797f670c2837> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Collection> .
<https://discovery.ucl.ac.uk/id/publication/ext-0b12c6835e67c7b73d5c797f670c2837> <http://xmlns.com/foaf/0.1/name> "ICALP 2021"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/publication/ext-0b12c6835e67c7b73d5c797f670c2837> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/ontology/bibo/status> <http://purl.org/ontology/bibo/status/published> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-5f02d9a293b56ba686f0169fef7f1c2a> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10152229#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10152229#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-5f02d9a293b56ba686f0169fef7f1c2a> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-232ce58bd75969cff17c06128d1eda11> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10152229#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10152229#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-232ce58bd75969cff17c06128d1eda11> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-690594a48e2a2df9106c52f26d4d23c5> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10152229#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10152229#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-690594a48e2a2df9106c52f26d4d23c5> .
<https://discovery.ucl.ac.uk/id/person/ext-690594a48e2a2df9106c52f26d4d23c5> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-690594a48e2a2df9106c52f26d4d23c5> <http://xmlns.com/foaf/0.1/givenName> "Shay"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-690594a48e2a2df9106c52f26d4d23c5> <http://xmlns.com/foaf/0.1/familyName> "Vargaftik"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-690594a48e2a2df9106c52f26d4d23c5> <http://xmlns.com/foaf/0.1/name> "Shay Vargaftik"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-5f02d9a293b56ba686f0169fef7f1c2a> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-5f02d9a293b56ba686f0169fef7f1c2a> <http://xmlns.com/foaf/0.1/givenName> "Ran"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-5f02d9a293b56ba686f0169fef7f1c2a> <http://xmlns.com/foaf/0.1/familyName> "Ben-Basat"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-5f02d9a293b56ba686f0169fef7f1c2a> <http://xmlns.com/foaf/0.1/name> "Ran Ben-Basat"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-232ce58bd75969cff17c06128d1eda11> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-232ce58bd75969cff17c06128d1eda11> <http://xmlns.com/foaf/0.1/givenName> "Michael"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-232ce58bd75969cff17c06128d1eda11> <http://xmlns.com/foaf/0.1/familyName> "Mitzenmacher"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-232ce58bd75969cff17c06128d1eda11> <http://xmlns.com/foaf/0.1/name> "Michael Mitzenmacher"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/ontology/bibo/presentedAt> <https://discovery.ucl.ac.uk/id/event/ext-92211555b56423befe894aa26b129523> .
<https://discovery.ucl.ac.uk/id/event/ext-92211555b56423befe894aa26b129523> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Conference> .
<https://discovery.ucl.ac.uk/id/event/ext-92211555b56423befe894aa26b129523> <http://purl.org/dc/terms/title> "The 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/EPrint> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/ProceedingsSectionEPrint> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/repository> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1474780> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1474780> <http://www.w3.org/2000/01/rdf-schema#label> "How to send a real number using a single bit (and some shared randomness) (Text)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://purl.org/dc/elements/1.1/hasVersion> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasPublished> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1474780> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10152229/1/LIPIcs-ICALP-2021-25.pdf> .
<https://discovery.ucl.ac.uk/id/document/1474780> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10152229/1/LIPIcs-ICALP-2021-25.pdf> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/1/LIPIcs-ICALP-2021-25.pdf> <http://www.w3.org/2000/01/rdf-schema#label> "LIPIcs-ICALP-2021-25.pdf"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1476704> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://www.w3.org/2000/01/rdf-schema#label> "How to send a real number using a single bit (and some shared randomness) (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://eprints.org/relation/isIndexCodesVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10152229/2/indexcodes.txt> .
<https://discovery.ucl.ac.uk/id/document/1476704> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10152229/2/indexcodes.txt> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/2/indexcodes.txt> <http://www.w3.org/2000/01/rdf-schema#label> "indexcodes.txt"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1476705> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://www.w3.org/2000/01/rdf-schema#label> "How to send a real number using a single bit (and some shared randomness) (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://eprints.org/relation/islightboxThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10152229/3/lightbox.jpg> .
<https://discovery.ucl.ac.uk/id/document/1476705> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10152229/3/lightbox.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/3/lightbox.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "lightbox.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1476706> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://www.w3.org/2000/01/rdf-schema#label> "How to send a real number using a single bit (and some shared randomness) (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://eprints.org/relation/ispreviewThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10152229/4/preview.jpg> .
<https://discovery.ucl.ac.uk/id/document/1476706> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10152229/4/preview.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/4/preview.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "preview.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1476707> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://www.w3.org/2000/01/rdf-schema#label> "How to send a real number using a single bit (and some shared randomness) (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://eprints.org/relation/ismediumThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10152229/5/medium.jpg> .
<https://discovery.ucl.ac.uk/id/document/1476707> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10152229/5/medium.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/5/medium.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "medium.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1476708> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://www.w3.org/2000/01/rdf-schema#label> "How to send a real number using a single bit (and some shared randomness) (Other)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://eprints.org/relation/issmallThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/1474780> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://eprints.org/ontology/hasFile> <https://discovery.ucl.ac.uk/id/eprint/10152229/6/small.jpg> .
<https://discovery.ucl.ac.uk/id/document/1476708> <http://purl.org/dc/terms/hasPart> <https://discovery.ucl.ac.uk/id/eprint/10152229/6/small.jpg> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/6/small.jpg> <http://www.w3.org/2000/01/rdf-schema#label> "small.jpg"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10152229> <http://www.w3.org/2000/01/rdf-schema#seeAlso> <https://discovery.ucl.ac.uk/id/eprint/10152229/> .
<https://discovery.ucl.ac.uk/id/eprint/10152229/> <http://purl.org/dc/elements/1.1/title> "HTML Summary of #10152229 \n\nHow to send a real number using a single bit (and some shared randomness)\n\n" .
<https://discovery.ucl.ac.uk/id/eprint/10152229/> <http://purl.org/dc/elements/1.1/format> "text/html" .
<https://discovery.ucl.ac.uk/id/eprint/10152229/> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10152229> .