## Abstract

Motivated by the study of deletion channels, this paper presents improved bounds on the number of subsequences obtained from a binary string X of length n under t deletions. It is known that the number of subsequences in this setting strongly depends on the number of runs in the string X; where a run is a maximal substring of the same character. Our improved bounds are obtained by a structural analysis of the family of r-run strings X, an analysis in which we identify the extremal strings with respect to the number of subsequences. Specifically, for every r, we present r-run strings with the minimum (respectively maximum) number of subsequences under any t deletions; we perform an exact analysis of the number of subsequences of these extremal strings; and show that this number can be calculated in polynomial time.

Original language | English |
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Article number | 7061929 |

Pages (from-to) | 2300-2312 |

Number of pages | 13 |

Journal | IEEE Transactions on Information Theory |

Volume | 61 |

Issue number | 5 |

DOIs | |

State | Published - 1 May 2015 |

### Bibliographical note

Publisher Copyright:© 1963-2012 IEEE.

## Keywords

- Channel coding
- binary codes
- error correction codes