### Abstract

In this correspondence, we consider a wireless sensor network consisting of n sensors, and each sensor has a measurement, which is an integer value belonging to the set {0,⋯,m-1}, so that it can be represented by [log_{2} m] bits. The network has a special node called the fusion center whose goal is to compute a symmetric function of these measurements. The problem studied is to minimize the total transmission energy used by the network when computing this function, subject to the constraint that this computation be correct with high probability. We assume the wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses r^{alpha} units of energy to transmit each bit, where r is the transmission range of the sensor. For constant m, the main result in this correspondence is an algorithm whose energy usage is κ ⌈log_{2} m⌉ n(log log n) (8 √ n/log n)^{α}, where κ = ⌈ 4/-log(4p(1-p))⌉. Then, we consider the case where the sensor network observes N events. In this case, we demonstrate a network algorithm which has energy usage Θ(n(√n/log n)α) per event if the number of events satisfies N = Ω(loglog n).

Original language | English (US) |
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Pages (from-to) | 4826-4833 |

Number of pages | 8 |

Journal | IEEE Transactions on Information Theory |

Volume | 53 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2007 |

### Keywords

- Binary symmetric channel
- Function computation
- Reception diversity
- Sensor network
- Wireless network

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*53*(12), 4826-4833. https://doi.org/10.1109/TIT.2007.909156