Coding for Interactive Communication Correcting Insertions and Deletions

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 <italic>insertions</italic> and <italic>deletions</italic> 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 tolerates noise rates of up to <inline-formula> <tex-math notation="LaTeX">$1/18- \varepsilon $ </tex-math></inline-formula>. To this end, we develop a novel primitive we name <italic>edit-distance tree code</italic>. The edit-distance tree code is carefully designed to replace the Hamming distance constraints in Schulman’s tree codes (<italic>IEEE Trans. Inf. Theory</italic>, 1996), with a stronger edit-distance requirement.

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