Coding for interactive communication correcting insertions and deletions

TL;DR

This paper introduces a novel interactive coding scheme capable of correcting insertions and deletions in noisy communication channels, achieving constant rate and resilience up to 1/18 noise rate by developing the new primitive called edit distance tree code.

Contribution

It presents the first interactive coding scheme with constant rate that corrects insertions and deletions, introducing the concept of edit distance tree codes for synchronization.

Findings

Achieves noise resilience up to 1/18 with constant rate

Develops the novel primitive of edit distance tree codes

Addresses synchronization issues in interactive communication

Abstract

We consider the question of interactive communication, in which two remote parties perform a computation while their communication channel is (adversarially) noisy. We extend here the discussion into a more general and stronger class of noise, namely, we allow the channel to perform insertions and deletions of symbols. These types of errors may bring the parties "out of sync", so that there is no consensus regarding the current round of the protocol. In this more general noise model, we obtain the first interactive coding scheme that has a constant rate and resists noise rates of up to $1/18-\varepsilon$. To this end we develop a novel primitive we name edit distance tree code. The edit distance tree code is designed to replace the Hamming distance constraints in Schulman's tree codes (STOC 93), with a stronger edit distance requirement. However, the straightforward generalization of tree codes to edit distance does not seem to yield a primitive that suffices for communication in the presence of synchronization problems. Giving the "right" definition of edit distance tree codes is a main conceptual contribution of this work.