Capacity regions for linear and abelian network codes
Capacity regions for linear and abelian network codes
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线性和阿贝尔网络码的容量区域
DOI：
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发表时间：
2007
期刊：
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通讯作者：
T. Chan
中科院分区：
文献类型：
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作者：
T. Chan
尽管在一般多播场景中证明了线性网络代码次优，但由于使用线性网络代码而导致的吞吐量丢失仍然未知。本文试图通过识别线性网络代码的容量区域来研究吞吐量的损失。我们证明，可以通过将网络引起的一组超平面和所有线性代表性熵函数集的凸锥闭合来识别容量区域。我们还将网络编码能力区域的研究扩展到包含线性网络代码作为子类的Abelian网络代码。对于两个多播会话的情况，我们获得了内部结合，可以利用可表示的熵函数的凸面闭合。
While linear network codes are proved suboptimal in general multicast scenarios, the loss of throughput due to the use of linear network codes is still unknown. This paper attempts to investigate the loss in throughput by identifying the capacity regions for linear network codes. We prove that the capacity region can be identified by taking intersection of a set of hyperplanes induced by the network and the convex cone closure of the set of all linear representable entropy functions. We also extend the study of network coding capacity region to abelian network codes which contain linear network codes as a subclass. For the case of two multicast sessions, we obtain an inner bound making use of the convex closure of entropy functions which are abelian group representable.