Abstract
In the (deletion-channel) trace reconstruction problem, there is an unknown
Previously, the best known algorithm for the trace reconstruction problem was due to Holenstein et al. [in Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms 389–398 (2008) ACM]; it uses
In this paper, we improve both of these results, obtaining matching upper and lower bounds for mean-based trace reconstruction. For any constant deletion rate
Our proofs involve estimates for the maxima of Littlewood polynomials on complex disks. We show that these techniques can also be used to perform trace reconstruction with random insertions and bit-flips in addition to deletions. We also find a surprising result: for deletion probabilities
Citation
Anindya De. Ryan O’Donnell. Rocco A. Servedio. "Optimal mean-based algorithms for trace reconstruction." Ann. Appl. Probab. 29 (2) 851 - 874, April 2019. https://doi.org/10.1214/18-AAP1394
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