Abhishek Jain
ABSTRACT
The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 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 multi-party setting. We show how to convert any (non-adaptive) $n$-party protocol into one that is resilient to Θ(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.
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Index Terms
- Interactive Coding for Multiparty Protocols
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