Error Correcting Codes for Interactive Channels

Error Correcting Codes (ECCs) address a fundamental question: how can we ensure reliable data transmission over unreliable channels? Since Shannon’s pioneering 1948 work, seven decades of research have created a rich theoretical framework with practical impacts across diverse fields.Today, communication systems are no longer just about transmitting information. Instead, they often involve interactive processes requiring multiple exchanges between participants, as seen in cloud computing, cryptographic protocols, and distributed systems.\begin{quote} \textbf{This proposal focuses on crafting interactive error-correcting codes and uncovering their fundamental limits.}\end{quote}Our research revisits the fundamental ECC problems in interactive contexts, aiming to address key challenges, including:\begin{enumerate} \item Determining the rate-distance trade-off for reliable data transmission. \item Investigating rate-distance trade-off for general interactive protocols \item Developing error-resilient protocols for distributed computing.\end{enumerate}We will explore both classical questions in interactive communication and uniquely interactive challenges, including the creation of adaptive coding schemes with enhanced performance over static alternatives.By integrating concepts from diverse fields, this work seeks to advance the interdisciplinary understanding of error correction in interactive settings.Given the success of classical ECCs and the growing importance of interaction in modern applications, we are confident that advancing the theory of \textbf{interactive error-correcting codes} will drive transformative progress.