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      Guess & Check Codes for Deletions, Insertions, and Synchronization

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          Abstract

          We consider the problem of constructing codes that can correct \(\delta\) deletions occurring in an arbitrary binary string of length \(n\) bits. Varshamov-Tenengolts (VT) codes are zero-error single deletion \((\delta=1)\) correcting codes, and have an asymptotically optimal redundancy. Finding similar codes for \(\delta \geq 2\) deletions is an open problem. We propose a new family of codes, that we call Guess & Check (GC) codes, that can correct, with high probability, up to \(\delta\) deletions occurring in a binary string. Moreover, we show that GC codes can also correct up to \(\delta\) insertions. GC codes are based on MDS codes and have an asymptotically optimal redundancy that is \(\Theta(\delta \log n)\). We provide deterministic polynomial time encoding and decoding schemes for these codes. We also describe the applications of GC codes to file synchronization.

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          Most cited references 10

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          Asymptotically good codes correcting insertions, deletions, and transpositions

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            On multiple insertion/deletion correcting codes

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              Capacity Upper Bounds for the Deletion Channel

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                Author and article information

                Journal
                2017-05-24
                1705.09569

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Submitted to IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1702.04466
                cs.IT math.IT

                Numerical methods, Information systems & theory

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