English

Non-binary Codes for Correcting a Burst of at Most t Deletions

Information Theory 2022-10-24 v1 math.IT

Abstract

The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most tt deletions in non-binary sequences. We first propose a non-binary code correcting a burst of at most 2 deletions for qq-ary alphabets. Afterwards, we extend this result to the case where the length of the burst can be at most tt where tt is a constant. Finally, we consider the setup where the sequences that are transmitted are permutations. The proposed codes are the largest known for their respective parameter regimes.

Keywords

Cite

@article{arxiv.2210.11818,
  title  = {Non-binary Codes for Correcting a Burst of at Most t Deletions},
  author = {Shuche Wang and Yuanyuan Tang and Jin Sima and Ryan Gabrys and Farzad Farnoud},
  journal= {arXiv preprint arXiv:2210.11818},
  year   = {2022}
}

Comments

20 pages. The paper has been submitted to IEEE Transactions on Information Theory. Furthermore, the paper was presented in part at the ISIT2021 and Allerton2022