### Abstract

A K-receiver degraded broadcast channel with secrecy outside a bounded range is studied, in which a transmitter sends K messages respectively to K receivers, and the channel quality gradually degrades from receiver K to receiver 1. Each receiver k is required to decode messages W_{1}, W_{k}, for 1 ≤ k ≤ K. Furthermore, each message W_{k} should be kept secure from receivers with two-level worse channel quality, i.e., receivers 1,., k-2. The secrecy capacity region is fully characterized. The achievable scheme designates one superposition layer to each message with random binning employed for each layer for protecting all upper-layer messages from lower-layer receivers. Furthermore, the scheme allows adjacent layers to share rates so that part of the rate of each message can potentially be shared with its immediate upper-layer message to enlarge the rate region. More importantly, an induction approach is developed to perform Fourier-Motzkin elimination over 2K variables among Θ(K^{2}) bounds to obtain a close-form achievable rate region. A converse proof is developed that matches the achievable rate region, which involves recursive construction of the rate bounds.

Original language | English (US) |
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Title of host publication | 2016 IEEE Information Theory Workshop, ITW 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 31-35 |

Number of pages | 5 |

ISBN (Electronic) | 9781509010905 |

DOIs | |

State | Published - Oct 21 2016 |

Event | 2016 IEEE Information Theory Workshop, ITW 2016 - Cambridge, United Kingdom Duration: Sep 11 2016 → Sep 14 2016 |

### Publication series

Name | 2016 IEEE Information Theory Workshop, ITW 2016 |
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### Other

Other | 2016 IEEE Information Theory Workshop, ITW 2016 |
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Country | United Kingdom |

City | Cambridge |

Period | 9/11/16 → 9/14/16 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Software
- Signal Processing

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## Cite this

*2016 IEEE Information Theory Workshop, ITW 2016*(pp. 31-35). [7606790] (2016 IEEE Information Theory Workshop, ITW 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2016.7606790