Coded Trace Reconstruction. Cheraghchi, M., Gabrys, R., Milenkovic, O., & Ribeiro, J. IEEE Transactions on Information Theory, 66(10):6084-6103, 2020. Preliminary version in Proceedings of ITW 2019.
Coded Trace Reconstruction [link]Link  Coded Trace Reconstruction [link]Paper  doi  abstract   bibtex   
Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of coded trace reconstruction, the design and analysis of high-rate efficiently encodable codes that can be efficiently decoded with high probability from few reads (also called traces) corrupted by edit errors. Codes used in current portable DNA-based storage systems with nanopore sequencers are largely based on heuristics, and have no provable robustness or performance guarantees even for an error model with i.i.d. deletions and constant deletion probability. Our work is a first step towards the design of efficient codes with provable guarantees for such systems. We consider a constant rate of i.i.d. deletions, and perform an analysis of marker-based code-constructions. This gives rise to codes with redundancy $O(n/łog n)$ (resp. $O(n/łogłog n)$) that can be efficiently reconstructed from $\exp(O(łog^{2/3}n))$ (resp. $\exp(O(łogłog n)^{2/3})$) traces, where $n$ is the message length. Then, we give a construction of a code with $O(łog n)$ bits of redundancy that can be efficiently reconstructed from $\mathrm{poly}(n)$ traces if the deletion probability is small enough. Finally, we show how to combine both approaches, giving rise to an efficient code with $O(n/łog n)$ bits of redundancy which can be reconstructed from $\mathrm{poly}(łog n)$ traces for a small constant deletion probability.
@ARTICLE{ref:CGMR20,
  author =	 {Mahdi Cheraghchi and Ryan Gabrys and Olgica
                  Milenkovic and Jo\~{a}o Ribeiro},
  title =	 {Coded Trace Reconstruction},
  year =	 2020,
  journal =	 {IEEE Transactions on Information Theory},
  note =	 {Preliminary version in Proceedings of {ITW 2019}.},
  doi =		 {10.1109/TIT.2020.2996377},
  volume={66},
  number={10},
  pages={6084-6103},
  url_Link =	 {https://ieeexplore.ieee.org/document/9097932},
  url_Paper =	 {https://arxiv.org/abs/1903.09992},
  abstract =	 {Motivated by average-case trace reconstruction and
                  coding for portable DNA-based storage systems, we
                  initiate the study of \textit{coded trace
                  reconstruction}, the design and analysis of
                  high-rate efficiently encodable codes that can be
                  efficiently decoded with high probability from few
                  reads (also called \textit{traces}) corrupted by
                  edit errors. Codes used in current portable
                  DNA-based storage systems with nanopore sequencers
                  are largely based on heuristics, and have no
                  provable robustness or performance guarantees even
                  for an error model with i.i.d. deletions and
                  constant deletion probability. Our work is a first
                  step towards the design of efficient codes with
                  provable guarantees for such systems. We consider a
                  constant rate of i.i.d. deletions, and perform an
                  analysis of marker-based code-constructions. This
                  gives rise to codes with redundancy $O(n/\log n)$
                  (resp. $O(n/\log\log n)$) that can be efficiently
                  reconstructed from $\exp(O(\log^{2/3}n))$
                  (resp. $\exp(O(\log\log n)^{2/3})$) traces, where
                  $n$ is the message length. Then, we give a
                  construction of a code with $O(\log n)$ bits of
                  redundancy that can be efficiently reconstructed
                  from $\mathrm{poly}(n)$ traces if the deletion
                  probability is small enough. Finally, we show how to
                  combine both approaches, giving rise to an efficient
                  code with $O(n/\log n)$ bits of redundancy which can
                  be reconstructed from $\mathrm{poly}(\log n)$ traces
                  for a small constant deletion probability.  }
}

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