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Computing linear functions by linear coding over networks

By Rathinakumar Appuswamy and Massimo Franceschetti

Abstract

We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can compute linear functions using linear codes. We identify a class of linear functions that can be computed using linear codes in every network that satisfies a natural cut-based condition. Conversely, for another class of linear functions, we show that the cut-based condition does not guarantee the existence of a linear coding solution. For linear functions over the binary field, the two classes are complements of each other

Topics: Computer Science - Information Theory, Mathematics - Commutative Algebra
Year: 2011
OAI identifier: oai:arXiv.org:1102.4825
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