## Abstract

This paper considers a network of source nodes that transmit data packets to a destination node via relay nodes over erasure channels by using random linear network coding. The probability that the destination node will fail to recover the packets of all source nodes has been bounded and approximated in the literature for the case of relay nodes that randomly assign only nonzero values to the coefficients of linear combinations of data packets. The paper argues for the necessity of giving relay nodes the choice to also assign the zero value to coefficients when arithmetic operations are over finite fields of small size, e.g. GF(2). Alternative probability mass functions for the coefficients are considered, and expressions for the decoding failure probability are re-derived.

Original language | English |
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Title of host publication | 89th IEEE Vehicular Technology Conference |

Publisher | IEEE |

Number of pages | 5 |

ISBN (Electronic) | 978-1-7281-1217-6 |

DOIs | |

Publication status | Published - 27 Jun 2019 |

Externally published | Yes |

Event | 2019 IEEE 89th Vehicular Technology Conference - Kuala Lumpur, Malaysia Duration: 28 Apr 2019 → 1 May 2019 Conference number: 89 http://www.ieeevtc.org/vtc2019spring/ |

### Publication series

Name | |
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ISSN (Electronic) | 2577-2465 |

### Conference

Conference | 2019 IEEE 89th Vehicular Technology Conference |
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Abbreviated title | VTC2019-Spring |

Country/Territory | Malaysia |

City | Kuala Lumpur |

Period | 28/04/19 → 1/05/19 |

Internet address |