Maximal Noise in Interactive Communication Over Erasure Channels and Channels With Feedback

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 nonadaptive protocol can withstand is 1/3. In addition, we provide a simple and efficient nonadaptive coding scheme that succeeds as long as the fraction of noise is at most $1/3-\varepsilon $ . 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 coding scheme that withstands the optimal tolerable erasure rate of $1/2-\varepsilon $ [Franklin et al. , IEEE Trans. Info. Theory , 2015], but operates in a much simpler and more efficient way than the previous schemes. Our coding scheme works with an alphabet of size 4, in contrast to prior schemes in which the alphabet size grows as $\varepsilon \to 0$ . 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-\varepsilon $ .