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arXiv · 0811.0285

Some results on communicating the sum of sources over a network

Brijesh Kumar Rai·Bikash Kumar Dey·Abhay Karandikar
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Abstract

We consider the problem of communicating the sum of $m$ sources to $n$ terminals in a directed acyclic network. Recently, it was shown that for a network of unit capacity links with either $m=2$ or $n=2$, the sum of the sources can be communicated to the terminals if and only if every source-terminal pair is connected in the network. We show in this paper that for any finite set of primes, there exists a network where the sum of the sources can be communicated to the terminals only over finite fields of characteristic belonging to that set. As a corollary, this gives networks where the sum can not be communicated over any finite field even though every source is connected to every terminal.

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Brijesh Kumar Rai, Bikash Kumar Dey, Abhay Karandikar. 2008-11-03. Some results on communicating the sum of sources over a network. https://arxiv.org/abs/0811.0285

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