Efficient Interactive Coding against Adversarial Noise

In this work, we study the problem of constructing interactive protocols that are robust to noise, a problem that was originally considered in the seminal works of Schulman (FOCS ´92, STOC ´93), and has recently regained popularity. Robust interactive communication is the interactive analogue of error correcting codes: Given an interactive protocol which is designed to run on an error-free channel, construct a protocol that evaluates the same function (or, more generally, simulates the execution of the original protocol) over a noisy channel. As in (non-interactive) error correcting codes, the noise can be either stochastic, i.e. drawn from some distribution, or adversarial, i.e. arbitrary subject only to a global bound on the number of errors. We show how to efficiently simulate any interactive protocol in the presence of constant-rate adversarial noise, while incurring only a constant blow-up in the communication complexity (CC). Our simulator is randomized, and succeeds in simulating the original protocol with probability at least 1 - 2^-Ω(CC).