### Abstract

We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C_{2K}(d), and the capacity of the binary deletion channel with the same deletion probability, C_{2}(d), that is, C_{2K}(d) ≤ C_{2}(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0.

Original language | English (US) |
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Title of host publication | 2013 IEEE International Symposium on Information Theory, ISIT 2013 |

Pages | 2940-2944 |

Number of pages | 5 |

DOIs | |

State | Published - Dec 19 2013 |

Event | 2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey Duration: Jul 7 2013 → Jul 12 2013 |

### Publication series

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

### Other

Other | 2013 IEEE International Symposium on Information Theory, ISIT 2013 |
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Country | Turkey |

City | Istanbul |

Period | 7/7/13 → 7/12/13 |

### ASJC Scopus subject areas

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

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## Cite this

*2013 IEEE International Symposium on Information Theory, ISIT 2013*(pp. 2940-2944). [6620764] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620764