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arXiv 0904.2401cs.ITmath.IT
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线性确定性中继网络的组合研究

A Combinatorial Study of Linear Deterministic Relay Networks

S. M. Sadegh Tabatabaei Yazdi, Serap A. Savari

摘要:

在过去的几年里,中继信道的所谓的“线性确定性”模型作为研究无线通信网络上的信息流的一种手段已经得到普及,并且这种方法推广了有线网络的模型,有线网络是网络优化中的标准。最近的工作扩展著名的最大流/最小割定理的能力,单播会话的线性确定性中继网络,这是由分层有向图建模。这一结果首先证明了一个随机编码方案在大块的传输信号。我们证明了同样的结果与一个简单的,确定性的,多项式时间算法,作为输入的一个单一的传输信号,而不是一个长的信号块。我们的容量实现传输方案的两层网络需要扩展的一维Rado-Hall横截定理的行划分矩阵的行的独立子集到一个二维的变化的块矩阵。为了将我们的方法推广到更大的网络,我们使用子模块的能力,我们的模型,并表明我们完整的传输方案可以通过求解两个多拟阵的交集的线性规划。我们证明了我们的传输方案可以实现最大流/最小割能力,通过应用埃德蒙兹定理,这样的线性规划。我们使用标准的次模函数最小化技术的一部分,我们的多项式时间算法来构建我们的能力实现传输方案。

英文摘要:

In the last few years the so--called "linear deterministic" model of relay channels has gained popularity as a means of studying the flow of information over wireless communication networks, and this approach generalizes the model of wireline networks which is standard in network optimization. There is recent work extending the celebrated max--flow/min--cut theorem to the capacity of a unicast session over a linear deterministic relay network which is modeled by a layered directed graph. This result was first proved by a random coding scheme over large blocks of transmitted signals. We demonstrate the same result with a simple, deterministic, polynomial--time algorithm which takes as input a single transmitted signal instead of a long block of signals. Our capacity-achieving transmission scheme for a two--layer network requires the extension of a one--dimensional Rado--Hall transversal theorem on the independent subsets of rows of a row--partitioned matrix into a two--dimensional variation for block matrices. To generalize our approach to larger networks we use the submodularity of the capacity of a cut for our model and show that our complete transmission scheme can be obtained by solving a linear program over the intersection of two polymatroids. We prove that our transmission scheme can achieve the max-flow/min-cut capacity by applying a theorem of Edmonds about such linear programs. We use standard submodular function minimization techniques as part of our polynomial--time algorithm to construct our capacity-achieving transmission scheme.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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