## Abstract

Two sensors obtain data vectors x and y, respec- tively, and transmit real vectors m1(x), and m2(y), respectively, to a fusion center. We obtain tight lower bounds on the number of messages (the sum of the dimensions of m1and m2) that have to be transmitted for the fusion center to be able to evaluate a given function f(x), y). When the function f is linear, we show that these bounds are effectively computable. Certain decentralized estimation problems can be cast in our framework and are discussed in some detail. In particular, we consider the case where x and y are random variables representing noisy measurements and f(x,y) = E[z x,y], where z is a random variable to be estimated. Furthermore, we establish that a standard method for combining decentralized estimates of Gaussian random variables has nearly optimal communication requirements.

Original language | English (US) |
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Pages (from-to) | 1551-1563 |

Number of pages | 13 |

Journal | IEEE Transactions on Information Theory |

Volume | 40 |

Issue number | 5 |

DOIs | |

State | Published - Sep 1994 |

### Bibliographical note

Funding Information:Manuscript received October 10, 1991; revised November 5, 1993. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant OPG0090391 and by the Army Research Office under Contract DAfL03-86-K-0171. Z.-Q. Luo is with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ont. U S 4L7, Canada. J. N. Tsitsiklis is with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139. IEEE Log Number 9405087.

## Keywords

- Decentralized estimation
- communication complexity
- data fusion
- distributed computation
- lower bounds