Computing linear functions by linear coding over networks
Information Theory
2011-02-24 v1 Commutative Algebra
math.IT
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.
Cite
@article{arxiv.1102.4825,
title = {Computing linear functions by linear coding over networks},
author = {Rathinakumar Appuswamy and Massimo Franceschetti},
journal= {arXiv preprint arXiv:1102.4825},
year = {2011}
}