### Abstract

We introduce a new variant of the k-deck problem, which in its traditional formulation asks for determining the smallest k that allows one to reconstruct any binary sequence of length n from the multiset of its k-length subsequences. In our version of the problem, termed the hybrid k-deck problem, one is given a certain number of special subsequences of the sequence of length n - t, t > 0, and the question of interest is to determine the smallest value of k such that the k-deck, along with the subsequences, allows for reconstructing the original sequence in an error-free manner. We first consider the case that one is given a single subsequence of the sequence of length n - t, obtained by deleting zeros only, and seek the value of k that allows for hybrid reconstruction. We prove that in this case, k [log t + 2, min{t + 1, O(√n)}]. We then proceed to extend the single-subsequence setup to the case where one is given M subsequences of length n - t obtained by deleting zeroes only. In this case, we first aggregate the asymmetric traces and then invoke the single-trace results. The analysis and problem at hand are motivated by nanopore sequencing problems for DNA-based data storage.

Original language | English (US) |
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Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1306-1310 |

Number of pages | 5 |

ISBN (Electronic) | 9781509040964 |

DOIs | |

State | Published - Aug 9 2017 |

Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
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Country | Germany |

City | Aachen |

Period | 6/25/17 → 6/30/17 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2017 IEEE International Symposium on Information Theory, ISIT 2017*(pp. 1306-1310). [8006740] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006740