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- W3198708829 abstract "The trace reconstruction problem studies the number of noisy samples needed to recover an unknown string <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$mathrm{x} in {0,1}^{n}$</tex> with high probability, where the samples are independently obtained by passing x through a random deletion channel with deletion probability <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$q$</tex> . The problem is receiving significant attention recently due to its applications in DNA sequencing and DNA storage. Yet, there is still an exponential gap between upper and lower bounds for the trace reconstruction problem. In this paper we study the trace reconstruction problem when x is confined to an edit distance ball of radius <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k$</tex> , which is essentially equivalent to distinguishing two strings with edit distance at most <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k$</tex> . It is shown that <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n^{O(k)}$</tex> samples suffice to achieve this task with high probability." @default.
- W3198708829 created "2021-09-13" @default.
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- W3198708829 date "2021-07-12" @default.
- W3198708829 modified "2023-10-02" @default.
- W3198708829 title "Trace Reconstruction with Bounded Edit Distance" @default.
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- W3198708829 doi "https://doi.org/10.1109/isit45174.2021.9518244" @default.
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