Binary Interactive Error Resilience Beyond ${{}^{1}}\!/\!_{8}$ (or why $({{}^{1}}\!/\!_{2})^{3} > {{}^{1}}\!/\!_{8})$

Interactive error correcting codesInteractive 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 is1/4. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to1/2 fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to5/39 >1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.