Maximal Noise in Interactive Communication over Erasure Channels and Channels with Feedback

TL;DR

This paper establishes tight bounds on the maximum noise levels that interactive communication protocols can tolerate over noisy channels with feedback and erasures, providing simple, efficient protocols that achieve these bounds.

Contribution

It introduces tight bounds on noise resilience for interactive protocols with feedback and designs simple protocols matching these bounds across different channel models.

Findings

Maximum noise fraction resistant is 1/3 for channels with feedback.

Optimal erasure rate of 1/2 - ε achieved with a simple protocol.

Binary erasure channel protocol tolerates up to 1/3 - ε erasure rate.

Abstract

We provide tight upper and lower bounds on the noise resilience of interactive communication over noisy channels with feedback. In this setting, we show that the maximal fraction of noise that any robust protocol can resist is 1/3. Additionally, we provide a simple and efficient robust protocol that succeeds as long as the fraction of noise is at most 1/3 - \epsilon. Surprisingly, both bounds hold regardless of whether the parties send bits or symbols from an arbitrarily large alphabet. We also consider interactive communication over erasure channels. We provide a protocol that matches the optimal tolerable erasure rate of 1/2 - \epsilon of previous protocols (Franklin et al., CRYPTO '13) but operates in a much simpler and more efficient way. Our protocol works with an alphabet of size 4, in contrast to prior protocols in which the alphabet size grows as epsilon goes to zero. Building on the above algorithm with a fixed alphabet size, we are able to devise a protocol for binary erasure channels that tolerates erasure rates of up to 1/3 - \epsilon.