Interactive coding, pioneered by Schulman (FOCS 1992, STOC 1993), is concerned with making communication protocols resilient to adversarial noise. The canonical model allows the adversary to alter a small constant fraction of symbols, chosen at the adversary's discretion, as they pass through the communication channel. Braverman, Gelles, Mao, and Ostrovsky (2015) proposed a far-reaching generalization of this model, whereby the adversary can additionally manipulate the channel by removing and inserting symbols. For any 0,"> 0 they showed how to faithfully simulate any protocol in this model with corruption rate up to 1 18 − using a constant-size alphabet and a constant-factor overhead in communication.

We give an optimal simulation of any protocol in this generalized model of substitutions, insertions, and deletions, tolerating a corruption rate up to 1 4 − while keeping the alphabet to a constant size and the communication overhead to a constant factor. Our corruption tolerance matches an impossibility result for corruption rate 1 4 which holds even for substitutions alone (Braverman and Rao, STOC 2011).