Distributed Lossy Averaging

In this paper, an information theoretic formulation of the distributed averaging problem previously studied in computer science and control is presented. We assume a network with m nodes each observing a white Gaussian noise (WGN) source. The nodes communicate and perform local processing with the g...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 56; no. 7; pp. 3422 - 3437
Main Authors: Han-I Su, El Gamal, Abbas
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
A stars
Computer errors
Computer networks
Computer science
Consensus
Distortion
distributed averaging
Distributed computing
Gaussian
Gaussian noise
gossip algorithms
Information processing
Information science
Information systems
interactive communication
lossy source coding
Lower bounds
Mathematical analysis
Mathematical models
Networks
Normal distribution
Peer to peer computing
Protocol
Protocol (computers)
Protocols
Rate-distortion
Source coding
Upper bound
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:In this paper, an information theoretic formulation of the distributed averaging problem previously studied in computer science and control is presented. We assume a network with m nodes each observing a white Gaussian noise (WGN) source. The nodes communicate and perform local processing with the goal of computing the average of the sources to within a prescribed mean squared error distortion. The network rate distortion function R* (D) for a two-node network with correlated Gaussian sources is established. A general cutset lower bound on R*(D) is established and shown to be achievable to within a factor of 2 via a centralized protocol over a star network. A lower bound on the network rate distortion function for distributed weighted-sum protocols, which is larger in order than the cutset bound by a factor of log m, is established. An upper bound on the network rate distortion function for gossip-base weighted-sum protocols, which is only log log m larger in order than the lower bound for a complete graph network, is established. The results suggest that using distributed protocols results in a factor of log m increase in order relative to centralized protocols.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2010.2048474