Binary $t_1$-Deletion-$t_2$-Insertion-Burst Correcting Codes and Codes Correcting a Burst of Deletions
Zuo Ye, Ohad Elishco

TL;DR
This paper introduces new binary and non-binary burst error-correcting codes with reduced redundancy, improving existing constructions for correcting deletion and insertion bursts in data transmission.
Contribution
It provides novel constructions of binary and non-binary burst error-correcting codes with lower redundancy than previous methods.
Findings
Redundancy for binary $t_1$-deletion-$t_2$-insertion codes is at most $ ext{log}(n)+(t_1-t_2-1) ext{log} ext{log}(n)+O(1)$.
Improved binary codes correct a burst of 4 deletions with reduced redundancy.
New non-binary $b$-burst-deletion codes with redundancy at most $ ext{log}(n)+(b-1) ext{log} ext{log}(n)+O(1)$.
Abstract
We first give a construction of binary -deletion--insertion-burst correcting codes with redundancy at most , where . Then we give an improved construction of binary codes capable of correcting a burst of non-consecutive deletions, whose redundancy is reduced from to . Lastly, by connecting non-binary -burst-deletion correcting codes with binary -deletion--insertion-burst correcting codes, we give a new construction of non-binary -burst-deletion correcting codes with redundancy at most . This construction is different from previous results.
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Taxonomy
TopicsDNA and Biological Computing · Algorithms and Data Compression · Advanced biosensing and bioanalysis techniques
