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- W4296974972 abstract "In the trace reconstruction problem an unknown string ${bf x}=(x_0,dots,x_{n-1})in{0,1,...,m-1}^n$ is observed through the deletion channel, which deletes each $x_k$ with a certain probability, yielding a contracted string $widetilde{bf X}$. Earlier works have proved that if each $x_k$ is deleted with the same probability $qin[0,1)$, then $exp(O(n^{1/3}))$ independent copies of the contracted string $widetilde{bf X}$ suffice to reconstruct $bf x$ with high probability. We extend this upper bound to the setting where the deletion probabilities vary, assuming certain regularity conditions. First we consider the case where $x_k$ is deleted with some known probability $q_k$. Then we consider the case where each letter $zetain {0,1,...,m-1}$ is associated with some possibly unknown deletion probability $q_zeta$." @default.
- W4296974972 created "2022-09-25" @default.
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- W4296974972 date "2017-08-07" @default.
- W4296974972 modified "2023-09-26" @default.
- W4296974972 title "Trace reconstruction with varying deletion probabilities" @default.
- W4296974972 doi "https://doi.org/10.48550/arxiv.1708.02216" @default.
- W4296974972 hasPublicationYear "2017" @default.
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