Binary Interactive Error Resilience Beyond 1/8 (or why (½)3>1/8)

Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Research output: Contribution to journalArticlepeer-review

Abstract

Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that such codes can protect against? If the error-resilient protocol is allowed to communicate large (constant sized) symbols, Braverman and Rao (STOC, 2011) show that the maximum rate of corruptions that can be tolerated is 1/4. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to 1/8 fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the 1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to 5/39 > 1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.
Original languageEnglish GB
Pages (from-to)1-41
Number of pages1
JournalElectronic Colloquium on Computational Complexity
Volume28
StatePublished - 2021

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