## Abstract

This paper investigates the simplification problem in Gaussian Half-Duplex (HD) diamond networks. The goal is to answer the following question: what is the minimum (worst-case) fraction of the total HD capacity that one can always achieve by smartly selecting a subset of k relays, out of the N possible ones? We make progress on this problem for k = 1 and k = 2 and show that for N = k + 1, k ⋯ |1, 2} at least k/k+1 of the total HD capacity is always approximately (i.e., up to a constant gap) achieved. Interestingly, and differently from the Full-Duplex (FD) case, the ratio in HD depends on N, and decreases as N increases. For all values of N and k for which we derive worst case fractions, we also show these to be approximately tight. This is accomplished by presenting N-relay Gaussian HD diamond networks for which the best k-relay subnetwork has an approximate HD capacity equal to the worst-case fraction of the total approximate HD capacity. Moreover, we provide additional comparisons between the performance of this simplification problem for HD and FD networks, which highlight their different natures.

Original language | English (US) |
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Title of host publication | Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2589-2593 |

Number of pages | 5 |

ISBN (Electronic) | 9781509018062 |

DOIs | |

State | Published - Aug 10 2016 |

Event | 2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: Jul 10 2016 → Jul 15 2016 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2016-August |

ISSN (Print) | 2157-8095 |

### Other

Other | 2016 IEEE International Symposium on Information Theory, ISIT 2016 |
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Country | Spain |

City | Barcelona |

Period | 7/10/16 → 7/15/16 |

### Bibliographical note

Funding Information:The work of M. Cardone and C. Fragouli was partially funded by NSF under award number 1514531. The work of D. Tuninetti was partially funded by NSF under award number 1218635. M. Cardone would like to acknowledge insightful discussions with Yahya H. Ezzeldin

Publisher Copyright:

© 2016 IEEE.

Copyright:

Copyright 2017 Elsevier B.V., All rights reserved.