{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8091","name":"Communication with Partial Noiseless Feedback","abstract":"We introduce the notion of one-way communication schemes with partial noiseless feedback. In this setting, Alice wishes to communicate a message to Bob by using a communication scheme that involves sending a sequence of bits over a channel while receiving feedback bits from Bob for delta fraction of the transmissions. An adversary is allowed to corrupt up to a constant fraction of Alice's transmissions, while the feedback is always uncorrupted. Motivated by questions related to coding for interactive communication, we seek to determine the maximum error rate, as a function of 0 <= delta <= 1, such that Alice can send a message to Bob via some protocol with delta fraction of noiseless feedback. The case delta = 1 corresponds to full feedback, in which the result of Berlekamp ['64] implies that the maximum tolerable error rate is 1\/3, while the case delta = 0 corresponds to no feedback, in which the maximum tolerable error rate is 1\/4, achievable by use of a binary error-correcting code.\r\n\r\nIn this work, we show that for any delta in (0,1] and gamma in [0, 1\/3), there exists a randomized communication scheme with noiseless delta-feedback, such that the probability of miscommunication is low, as long as no more than a gamma fraction of the rounds are corrupted. Moreover, we show that for any delta in (0, 1] and gamma < f(delta), there exists a deterministic communication scheme with noiseless delta-feedback that always decodes correctly as long as no more than a gamma fraction of rounds are corrupted. Here f is a monotonically increasing, piecewise linear, continuous function with f(0) = 1\/4 and f(1) = 1\/3. Also, the rate of communication in both cases is constant (dependent on delta and gamma but independent of the input length).","keywords":["Communication with feedback","Interactive communication","Coding theory Digital"],"author":[{"@type":"Person","name":"Haeupler, Bernhard","givenName":"Bernhard","familyName":"Haeupler"},{"@type":"Person","name":"Kamath, Pritish","givenName":"Pritish","familyName":"Kamath"},{"@type":"Person","name":"Velingker, Ameya","givenName":"Ameya","familyName":"Velingker"}],"position":52,"pageStart":881,"pageEnd":897,"dateCreated":"2015-08-13","datePublished":"2015-08-13","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Haeupler, Bernhard","givenName":"Bernhard","familyName":"Haeupler"},{"@type":"Person","name":"Kamath, Pritish","givenName":"Pritish","familyName":"Kamath"},{"@type":"Person","name":"Velingker, Ameya","givenName":"Ameya","familyName":"Velingker"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.APPROX-RANDOM.2015.881","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6243","volumeNumber":40,"name":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX\/RANDOM 2015)","dateCreated":"2015-08-13","datePublished":"2015-08-13","editor":[{"@type":"Person","name":"Garg, Naveen","givenName":"Naveen","familyName":"Garg"},{"@type":"Person","name":"Jansen, Klaus","givenName":"Klaus","familyName":"Jansen"},{"@type":"Person","name":"Rao, Anup","givenName":"Anup","familyName":"Rao"},{"@type":"Person","name":"Rolim, Jos\u00e9 D. P.","givenName":"Jos\u00e9 D. P.","familyName":"Rolim"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8091","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6243"}}}