Publication
IEEE Trans. Inf. Theory
Paper

Computing linear functions by linear coding over networks

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Abstract

We consider the scenario in which a set of sources generates 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. © 1963-2012 IEEE.

Date

01 Jan 2014

Publication

IEEE Trans. Inf. Theory

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