Coding for Synthesis Defects
<|reference_start|>Coding for Synthesis Defects: Motivated by DNA based data storage system, we investigate the errors that occur when synthesizing DNA strands in parallel, where each strand is appended one nucleotide at a time by the machine according to a template supersequence. If there is a cycle such that the machine fails, then the strands meant to be appended at this cycle will not be appended, and we refer to this as a synthesis defect. In this paper, we present two families of codes correcting synthesis defects, which are t-known-synthesis-defect correcting codes and t-synthesis-defect correcting codes. For the first one, it is assumed that the defective cycles are known, and each of the codeword is a quaternary sequence. We provide constructions for this family of codes for t = 1, 2, with redundancy log 4 and log n+18 log 3, respectively. For the second one, the codeword is a set of M ordered sequences, and we give constructions for t = 1, 2 to show a strategy for constructing this family of codes. Finally, we derive a lower bound on the redundancy for single-known-synthesis-defect correcting codes, which assures that our construction is almost optimal.<|reference_end|>
@article{lu2024coding,
    title={Coding for Synthesis Defects},
    author={Ziyang Lu, Han Mao Kiah, Yiwei Zhang, Robert N. Grass, and Eitan
  Yaakobi},
    journal={arXiv preprint arXiv:2405.02080},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02080},
    primaryClass={cs.IT math.IT}
}