Communicating the sum of sources over a network
We consider a network (that is capable of network coding) with a set of sources and terminals, where each terminal is interested in recovering the sum of the sources. Considering directed acyclic graphs with unit capacity edges and independent, unit-entropy sources, we show the rate region when (a) there are two sources and n terminals, and (b) n sources and two terminals. In these cases as long as there exists at least one path from each source to each terminal we demonstrate that there exists a valid assignment of coding vectors to the edges such that the terminals can recover the sum of the sources.
This is a manuscript of a proceeding from the IEEE International Symposium on Information Theory (2008): 1646, doi:10.1109/ISIT.2008.4595267. Posted with permission.