A New Upper Bound on the Maximal Error Resilience of Interactive Error-Correcting Codes

Abstract: In an interactive error-correcting code (iECC), Alice and Bob engage in an interactive protocol with the goal of Alice communicating a message $x \in { 0, 1 }<sup>k$ to Bob in such a way that even if some fraction of the total communicated bits are corrupted, Bob can still determine $x$. It was shown in works by Gupta, Kalai, and Zhang (STOC 2022) and by Efremenko, Kol, Saxena, and Zhang (FOCS 2022) that there exist iECCs that are resilient to a larger fraction of errors than is possible in standard error-correcting codes without interaction. One major question in the study of iECCs is to determine the optimal error resilience achievable by an iECC. In the case of bit flip errors, it is known that an iECC can achieve $\frac14 + 10<sup>{-5}$ error resilience (Efremenko, Kol, Saxena, and Zhang), while the best known upper bound is $\frac27 \approx 0.2857$ (Gupta, Kalai, and Zhang). In this work, we improve upon the upper bound, showing that no iECC can be resilient to more than $\frac{13}{47} \approx 0.2766$ fraction of errors.