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A Deterministic Polynomial-Time Protocol for Synchronizing from Deletions

In this paper, we consider a synchronization problem between nodes $A$ and $B$ that are connected through a two--way communication channel. {Node $A$} contains a binary file $X$ of length $n$ and {node $B$} contains a binary file $Y$ that is generated by randomly deleting bits from $X$, by a small deletion rate $β$. The location of deleted bits is not known to either node $A$ or node $B$. We offer a deterministic synchronization scheme between nodes $A$ and $B$ that needs a total of $O(nβ\log \frac{1}β)$ transmitted bits and reconstructs $X$ at node $B$ with probability of error that is exponentially low in the size of $X$. Orderwise, the rate of our scheme matches the optimal rate for this channel.