TR21-051 Authors: Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Publication: 9th April 2021 07:15

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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.