Guess & Check Codes for Deletions, Insertions, and Synchronization

Serge Kas Hanna; Salim El Rouayheb

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arXiv · 1705.09569

Guess & Check Codes for Deletions, Insertions, and Synchronization

Serge Kas Hanna·Salim El Rouayheb

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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, dating back to 1965, are zero-error single deletion $(\delta=1)$ correcting codes, and have an asymptotically optimal redundancy. Finding similar codes for $\delta \geq 2$ deletions remains an open problem. In this work, we relax the standard zero-error (i.e., worst-case) decoding requirement by assuming that the positions of the $\delta$ deletions (or insertions) are independent of the codeword. Our contribution is a new family of explicit codes, that we call Guess & Check (GC) codes, that can correct with high probability up to a constant number of $\delta$ deletions (or insertions). GC codes are systematic; and have deterministic polynomial time encoding and decoding algorithms. We also describe the application of GC codes to file synchronization.

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Serge Kas Hanna, Salim El Rouayheb. 2017-05-24. Guess & Check Codes for Deletions, Insertions, and Synchronization. https://arxiv.org/abs/1705.09569

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