Polynomial-time trace reconstruction in the smoothed complexity model

@inproceedings{Chen2021PolynomialtimeTR,
  title={Polynomial-time trace reconstruction in the smoothed complexity model},
  author={Xianmiao Chen and Anindya De and Chin Ho Lee and R. Servedio and S. Sinha},
  booktitle={SODA},
  year={2021}
}
In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is sent through a probabilistic \emph{deletion channel} which independently deletes each bit with probability $\delta$ and concatenates the surviving bits, yielding a \emph{trace} of $x$. The problem is to reconstruct $x$ given independent traces. This problem has received much attention in recent years both in the worst-case setting where $x$ may be an arbitrary string in $\{0,1\}^n$ \cite{DOS17… Expand

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We improve the upper bound on worst case trace reconstruction from exp(O(n)) to exp(Õ(n)) for any deletion probability q ≤ 1 2 .
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