{"title":"Communicating the sum of sources in a 3-sources/3-terminals network; revisited","authors":"M. Langberg, A. Ramamoorthy","doi":"10.1109/ISIT.2010.5513422","DOIUrl":null,"url":null,"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.","PeriodicalId":92224,"journal":{"name":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Information Theory and its Applications. International Symposium on Information Theory and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2010.5513422","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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。