Distributed calculation of linear functions in noisy networks via linear iterations
Ημερομηνία
2008ISBN
978-1-4244-3124-3Source
Proceedings of the IEEE Conference on Decision and ControlProceedings of the IEEE Conference on Decision and Control
Pages
5462-5467Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
Given a fixed network where each node has some given initial value, and under the constraint that each node receives noisy transmissions from its immediate neighbors, we provide a distributed scheme for any node to calculate an unbiased estimate of an arbitrary linear function of the initial values. Our scheme consists of a linear iteration where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We show that after repeating this process with almost any set of weights for a finite number of time-steps (upper bounded by the size of the network), any node in the network will be able to calculate an unbiased estimate of any linear function by taking a linear combination of the values that it sees over the course of the linear iteration. For a given set of weights, this linear combination can also be optimized to minimize the variance of the unbiased estimate calculated by each node. © 2008 IEEE.
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