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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
