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)
.