Communicating the sum of sources in a 3-sources/3-terminals network; revisited

M. Langberg, A. Ramamoorthy
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引用次数: 8

Abstract

We consider the problem of multicasting sums over directed acyclic networks with unit capacity edges. A set of source nodes si observe independent unit-entropy source processes X i and want to communicate Σ X i to a set of terminals t j . Previous work on this problem has established necessary and sufficient conditions on the s i -t j connectivity in the case when there are two sources or two terminals (Ramamoorthy '08), and in the case of three sources and three terminals (Langberg-Ramamoorthy '09). In particular the latter result establishes that each terminal can recover the sum if there are two edge disjoint paths between each s i -t j pair. In this work, we provide a new and significantly simpler proof of this result, and introduce techniques that may be of independent interest in other network coding problems.
通信3源/3端网络中的源和;重新审视
研究具有单位容量边的有向无环网络上的组播和问题。一组源节点si观察到独立的单位熵源进程X i,并希望将Σ X i与一组终端t j通信。先前对该问题的研究已经建立了两个源或两个终端(Ramamoorthy '08)和三个源和三个终端(Langberg-Ramamoorthy '09)的情况下s i -t j连接的充分必要条件。特别是后一种结果表明,如果每个s i -t j对之间存在两条边不相交的路径,则每个端点都可以恢复和。在这项工作中,我们为这一结果提供了一种新的、简单得多的证明,并引入了可能对其他网络编码问题独立感兴趣的技术。
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