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Computing Linear Functions by Linear Coding Over Networks | IEEE Journals & Magazine | IEEE Xplore

Computing Linear Functions by Linear Coding Over Networks


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 formulat...Show More

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.
Published in: IEEE Transactions on Information Theory ( Volume: 60, Issue: 1, January 2014)
Page(s): 422 - 431
Date of Publication: 27 September 2013

ISSN Information:


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