Computer Science – Information Theory
Scientific paper
2010-12-23
Computer Science
Information Theory
Scientific paper
Traditionally, communication networks are modeled and analyzed in terms of information flows in graphs. In this paper, we introduce a novel symbolic approach to communication networks, where the topology of the underlying network is contained in a set of formal terms from logic. In order to account multi-user or dynamic networks, we allow distributed coding functions, which represent the same node in different situations. For any choice of coding functions we associate a measure of performance referred to as the dispersion. We thus show that many communication problems can be recast as dispersion problems in this setup. For a large class of measures containing the dispersion, we first show that the maximum flow of information transmitted to the users is asymptotically equal to the min-cut of the term set, which represents the number of degrees of freedom of that term set. On the other hand, there are information measures for which the maximum flow may not attend the min-cut. Second, we derive a general principle for many-to-many cast communications in dynamic multi-user networks. We prove that if each demand can be satisfied locally, then they can all be achieved globally, which happens when the respective min-cuts satisfy the demands.
Gadouleau Maximilien
Riis Soren
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