Communication complexity of edit resilient synchronization

Supposing we have two strings $A$ and $B$ that are both edit distance $\tau$ from each other at two different sites is there a communication complexity model where synchronizing such strings have been studied?

Supposing before edit errors assume $A$ and $B$ have been distorted by some additive noise is there a communication complexity model where synchronizing such strings have been studied?

I am looking for reasonable upper and lower bound models. I am also looking for references and survey of bounds.