Papers › Guess & Check Codes for Deletions, Insertions, and Synchronization
Guess & Check Codes for Deletions, Insertions, and Synchronization
Serge Kas Hanna, Salim El Rouayheb
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We consider the problem of constructing codes that can correct δ deletions occurring in an arbitrary binary string of length n bits. Varshamov-Tenengolts (VT) codes, dating back to 1965, are zero-error single deletion (δ=1) correcting codes, and have an asymptotically optimal redundancy. Finding similar codes for δ≥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 δ 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 δ 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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