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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| Vydáno v: | IEEE transactions on information theory Ročník 56; číslo 7; s. 3422 - 3437 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.07.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | 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 $R^{ast }(D)$ for a two-node network with correlated Gaussian sources is established. A general cutset lower bound on $R^{ast }(D)$ 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. [PUBLICATION ABSTRACT] 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. 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 ast ( D ) for a two-node network with correlated Gaussian sources is established. A general cutset lower bound on R ast ( 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. |
| Author | Han-I Su El Gamal, Abbas |
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| SubjectTerms | 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 |
| Title | Distributed Lossy Averaging |
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