Interactive Coding for Multiparty Protocols.

The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOGS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant-fraction of adversarial error, while blowing up the communication by only a constant factor.In this work we extend the work of Schulman to the multiparty setting. We show how to convert any (non-adaptive) n-party protocol into one that is resilient to Theta(1/n)-fraction of adversarial error, while blowing up the communication by only a constant factor.One might hope to get resilience to constant-fraction of errors, by restricting the adversary's error distribution, and allowing him to make at most a constant-fraction of errors per party. We present a black-box lower bound, showing that we cannot be resilient to such adversarial errors, even if we increase the communication by an arbitrary polynomial factor, assuming the error-resilient protocol has a fixed (non-adaptive) speaking order.