线性和阿贝尔网络码的容量区域

T. Chan
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引用次数: 24

摘要

虽然线性网络编码在一般组播场景中被证明是次优的,但由于使用线性网络编码而导致的吞吐量损失仍然未知。本文试图通过识别线性网络码的容量区域来研究吞吐量的损失。我们证明了容量区域可以通过取由网络导出的一组超平面与所有线性可表示熵函数集合的凸锥闭包的交集来识别。我们还将网络编码容量域的研究扩展到包含线性网络码的阿贝尔网络码。对于两个组播会话,我们利用熵函数的凸闭包得到了一个内界,而熵函数是阿贝尔群可表示的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Capacity regions for linear and abelian network codes
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.
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