## 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 | 2019 IEEE 89th Vehicular Technology Conference, VTC Spring 2019 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781728112176 |

DOIs | |

Publication status | Published - Apr 2019 |

Event | 89th IEEE Vehicular Technology Conference, VTC Spring 2019 - Kuala Lumpur, Malaysia Duration: 28 Apr 2019 → 1 May 2019 |

### Publication series

Name | IEEE Vehicular Technology Conference |
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Volume | 2019-April |

ISSN (Print) | 1550-2252 |

### Conference

Conference | 89th IEEE Vehicular Technology Conference, VTC Spring 2019 |
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Country/Territory | Malaysia |

City | Kuala Lumpur |

Period | 28/04/19 → 1/05/19 |

### Bibliographical note

Publisher Copyright:© 2019 IEEE.

### Funding

VII. ACKNOWLEDGEMENTS This work was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) under Grant No. EP/R006385/1. Collaboration of the authors was facilitated by the Erasmus+ programme of the European Union.

Funders | Funder number |
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Engineering and Physical Sciences Research Council | EP/R006385/1 |

## Keywords

- Cooperative communication
- Decoding probability
- Random linear network coding
- Random matrices