Optimal Interactive Coding for Insertions, Deletions, and Substitutions

Abstract

Interactive coding, pioneered by Schulman (FOCS ’92, STOC ’93), 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 et al. proposed a far-reaching generalization of this model, whereby the adversary can additionally manipulate the channel by removing and inserting symbols. For any $\epsilon >0,$ they showed how to faithfully simulate any protocol in this model with corruption rate up to $1/18-\epsilon ,$ 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-\epsilon $ , while keeping the alphabet to a constant size and the communication overhead to a constant factor. This resolves a question due to Gelles (2015). Our corruption tolerance matches an impossibility result for corruption rate 1/4 which holds even for substitutions alone (Braverman and Rao, STOC ‘11).