Communicating the Sum of Sources Over a Network
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The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.
History
The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.
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1909-present
Historical Names
- Department of Electrical Engineering (1909-1985)
- Department of Electrical Engineering and Computer Engineering (1985-1995)
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- College of Engineering (parent college)
- Department of Physics and Electrical Engineering (predecessor)
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Abstract
We consider the network communication scenario, over directed acyclic networks with unit capacity edges in which a number of sources si each holding independent unit-entropy information Xi wish to communicate the sum ΣXi to a set of terminals tj. We show that in the case in which there are only two sources or only two terminals, communication is possible if and only if each source terminal pair si/tj is connected by at least a single path. For the more general communication problem in which there are three sources and three terminals, we prove that a single path connecting the source terminal pairs does not suffice to communicate ΣXi. We then present an efficient encoding scheme which enables the communication of ΣXi for the three sources, three terminals case, given that each source terminal pair is connected by two edge disjoint paths.
Comments
This is a manuscript of an article published as Ramamoorthy, Aditya, and Michael Langberg. "Communicating the sum of sources over a network." IEEE Journal on Selected Areas in Communications 31, no. 4 (2013): 655-665. DOI: 10.1109/JSAC.2013.130404. Posted with permission.