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 MoreMetadata
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)