Interactive communication with unknown noise rate

We describe an algorithm requiring no such knowledge, under the additional assumption that the channel connecting Alice and Bob is private. If an adversary flips T bits, our algorithm sends L+O(L(T+1)log⁡L+T) bits in expectation and succeeds with high probability in L. It does so without any a priori knowledge of T. Assuming a lower bound conjectured by Haeupler, our result is optimal up to logarithmic factors.