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- W3198809646 abstract "We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k$</tex> deletions occur in a window of size <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k$</tex> , where the positions of the deletions within this window are not necessarily consecutive. Localized deletions are thus a generalization of burst deletions that occur in consecutive positions. We present novel explicit codes that are efficiently encodable and decodable and can correct up to <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k$</tex> localized deletions. Furthermore, these codes have <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$log n+mathcal{O}(klog^{2}(klog n))$</tex> redundancy, where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n$</tex> is the length of the information message, which is asymptotically optimal in <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$n$</tex> for <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$k=o(log n/(loglog n)^{2})$</tex> ." @default.
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- W3198809646 date "2021-07-12" @default.
- W3198809646 modified "2023-10-06" @default.
- W3198809646 title "Optimal Codes Correcting Localized Deletions" @default.
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- W3198809646 doi "https://doi.org/10.1109/isit45174.2021.9518196" @default.
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