### Abstract

Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and for computing in an arbitrarily connected network of nodes. Specifically, we propose a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithms almost surely converge to a consensus. In addition, the random consensus value is, in expectation, equal to the desired value, i.e., the average of initial node measurements. However, the broadcast gossip algorithms do not converge to the initial average in absolute sense because of the fact that the sum is not preserved at every iteration. We provide theoretical results on the mean square error performance of the broadcast gossip algorithms. The results indicate that the mean square error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithms required to achieve a given distance to consensus through numerical simulations.

Original language | English (US) |
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Title of host publication | 2008 IEEE Information Theory Workshop, ITW |

Pages | 343-347 |

Number of pages | 5 |

DOIs | |

State | Published - Sep 22 2008 |

Externally published | Yes |

Event | 2008 IEEE Information Theory Workshop, ITW - Porto, Portugal Duration: May 5 2008 → May 9 2008 |

### Publication series

Name | 2008 IEEE Information Theory Workshop, ITW |
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### Other

Other | 2008 IEEE Information Theory Workshop, ITW |
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Country | Portugal |

City | Porto |

Period | 5/5/08 → 5/9/08 |

### Keywords

- Broadcasting
- Distributed average consensus
- Gossip algorithms
- Sensor networks

### ASJC Scopus subject areas

- Information Systems
- Electrical and Electronic Engineering

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## Cite this

*2008 IEEE Information Theory Workshop, ITW*(pp. 343-347). [4578682] (2008 IEEE Information Theory Workshop, ITW). https://doi.org/10.1109/ITW.2008.4578682