A Deterministic Polynomial-Time Protocol for Synchronizing from Deletions

TL;DR

This paper presents a deterministic, polynomial-time protocol for synchronizing binary files between two nodes over a channel with random deletions, achieving near-optimal communication efficiency with exponentially low error.

Contribution

It introduces a new deterministic synchronization scheme for deletion channels that operates in polynomial time and matches the optimal rate.

Findings

Requires O(nβ log(1/β)) bits transmitted

Reconstructs original file with exponentially low error

Achieves orderwise optimal rate for deletion synchronization

Abstract

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 $\beta$. 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 $O(n\beta\log \frac{1}{\beta})$ 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.