Coordination Capacity

• Published in: IEEE transactions on information theory Vol. 56; no. 9; pp. 4181 - 4206
• Main Authors: Cuff, P W, Permuter, H H, Cover, T M
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-09-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Coding, codes; Common randomness; Communication networks; Communications networks; Computer networks; Computer science; cooperation capacity; coordination capacity; Distributed computing; Distributed control; Exact sciences and technology; Information technology; Information theory; Information, signal and communications theory; Mutual information; Network coding; network dependence; Probability distribution; Random processes; Rate-distortion; Signal and communications theory; Source coding; strong Markov lemma; Systems, networks and services of telecommunications; task assignment; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Wyner common information; Source coding; Rate distortion theory; Joint distribution; Stochastic process; rate distortion; Common randomness; cooperation capacity; strong Markov lemma; Telecommunication network; network dependence; task assignment; Mutual information; Wyner common information; coordination capacity
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2010.2054651

We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates {R i ,j} between the nodes, we ask what is the set of all achievable joint distributions p(x 1 , ..., xm) of actions at the nodes of the network. Several networks are solved, including arbitrarily large cascade networks. Distributed cooperation can be the solution to many problems such as distributed games, distributed control, and establishing mutual information bounds on the influence of one part of a physical system on another.