Single-Deletion Single-Substitution Correcting Codes
Ilia Smagloy, Lorenz Welter, Antonia Wachter-Zeh, Eitan Yaakobi

TL;DR
This paper establishes bounds and constructs codes capable of correcting a single insertion or deletion along with a single substitution, advancing error correction in DNA storage and communication systems.
Contribution
It derives a non-asymptotic upper bound on code size and provides an explicit construction with low redundancy for single-deletion single-substitution correction.
Findings
Redundancy must be at least 2 log n for such codes.
Constructed codes have at most 6 log n + 8 redundancy bits.
Compared to previous 3-deletion correction codes, this is more efficient.
Abstract
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that can correct a single insertion or deletion along with a single substitution. A non-asymptotic upper bound on the size of single-deletion single-substitution correcting codes is derived, showing that the redundancy of such a code of length has to be at least . The bound is presented both for binary and non-binary codes while an extension to single deletion and multiple substitutions is presented for binary codes. An explicit construction of single-deletion single-substitution correcting codes with at most redundancy bits is derived. Note that the best known construction for this problem has to use 3-deletion correcting…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsDNA and Biological Computing · Advanced biosensing and bioanalysis techniques · Quantum-Dot Cellular Automata
