Multiple Criss-Cross Insertion and Deletion Correcting Codes
Lorenz Welter, Rawad Bitar, Antonia Wachter-Zeh, Eitan Yaakobi

TL;DR
This paper develops new codes capable of correcting multiple criss-cross insertions and deletions in arrays, providing bounds on redundancy and a construction method using binary deletion-correcting and Gabidulin codes.
Contribution
It introduces an equivalence between criss-cross insertions and deletions and proposes a code construction with bounded redundancy using systematic binary and Gabidulin codes.
Findings
Redundancy lower bound: $tn + t \,\log n - \log(t!)$
Existential code construction with redundancy $tn + \mathcal{O}(t^2 \log^2 n)$
Transformation of insertion/deletion correction to erasure correction using systematic codes
Abstract
This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of arrays affected by -criss-cross deletions defined as any combination of row and column deletions such that for a given . We show an equivalence between correcting -criss-cross deletions and -criss-cross insertions and show that a code correcting -criss-cross insertions/deletions has redundancy at least . Then, we present an existential construction of -criss-cross insertion/deletion correcting code with redundancy bounded from above by . The main ingredients of the presented code construction are systematic binary -deletion correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the…
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Taxonomy
TopicsDNA and Biological Computing · Advanced biosensing and bioanalysis techniques · Coding theory and cryptography
