Positive Rate Binary Interactive Error Correcting Codes Resilient to $>\frac{1}{2}$ 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 $\frac{1}{2}$. The work of \cite{GuptaTZ21} constructed the first $\mathsf{iECC}$ resilient to $>\frac{1}{2}$ 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 $>\frac{1}{2}$ adversarial erasures. For any $\epsilon >0$, our $\mathsf{iECC}$ is resilient to $\frac{6}{11}-\epsilon$ adversarial erasures and has size $O_{\epsilon }(n)$.

arXiv admin note: text overlap with arXiv:2111.04181