Positive Rate Binary Interactive Error Correcting Codes Resilient to $>\frac12$ Adversarial Erasures

Abstract

An interactive error correcting code ($\mathsf{iECC}$) is an interactive protocol with the guarantee that the receiver can correctly determine the sender's message, even in the presence of noise. This generalizes the concept of an error correcting code ($\mathsf{ECC}$), which is a non-interactive $\mathsf{iECC}$ that is known to have erasure resilience capped at $\frac12$. The work of \cite{GuptaTZ21} constructed the first $\mathsf{iECC}$ resilient to $> \frac12$ adversarial erasures. However, their $\mathsf{iECC}$ has communication complexity quadratic in the message size. In our work, we construct the first positive rate $\mathsf{iECC}$ resilient to $> \frac12$ adversarial erasures. For any $\epsilon > 0$, our $\mathsf{iECC}$ is resilient to $\frac6{11} - \epsilon$ adversarial erasures and has size $O_\epsilon(n)$.