
Polynomialtime trace reconstruction in the smoothed complexity model
In the trace reconstruction problem, an unknown source string x ∈{0,1}^n...
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Subpolynomial trace reconstruction for random strings and arbitrary deletion probability
The deletioninsertion channel takes as input a bit string x∈{0,1}^n, a...
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Efficient averagecase population recovery in the presence of insertions and deletions
Several recent works have considered the trace reconstruction problem, i...
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Beyond trace reconstruction: Population recovery from the deletion channel
Population recovery is the problem of learning an unknown distribution o...
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Population Recovery from the Deletion Channel: Nearly Matching Trace Reconstruction Bounds
The population recovery problem asks one to recover an unknown distribut...
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MeanBased Trace Reconstruction over Practically any ReplicationInsertion Channel
Meanbased reconstruction is a fundamental, natural approach to worstca...
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Coded trace reconstruction
Motivated by averagecase trace reconstruction and coding for portable D...
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Polynomialtime trace reconstruction in the low deletion rate regime
In the trace reconstruction problem, an unknown source string x ∈{0,1}^n is transmitted through a probabilistic deletion channel which independently deletes each bit with some fixed probability δ and concatenates the surviving bits, resulting in a trace of x. The problem is to reconstruct x given access to independent traces. Trace reconstruction of arbitrary (worstcase) strings is a challenging problem, with the current state of the art for poly(n)time algorithms being the 2004 algorithm of Batu et al. <cit.>. This algorithm can reconstruct an arbitrary source string x ∈{0,1}^n in poly(n) time provided that the deletion rate δ satisfies δ≤ n^(1/2 + ε) for some ε > 0. In this work we improve on the result of <cit.> by giving a poly(n)time algorithm for trace reconstruction for any deletion rate δ≤ n^(1/3 + ε). Our algorithm works by alternating an alignmentbased procedure, which we show effectively reconstructs portions of the source string that are not "highly repetitive", with a novel procedure that efficiently determines the length of highly repetitive subwords of the source string.
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