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A Theory of Network Equivalence – Part II: Multiterminal Channels

机译：网络对等理论–第二部分：多终端通道

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摘要

A technique for bounding the capacities of networks of independent channels is introduced. Parts I and II treat point-to-point and multiterminal channels, respectively. Bounds are derived using a new tool called a bounding model. Channel 1 is an upper (lower) bounding model for channel 2 if replacing channel 2 by channel 1 in any network yields a new network whose capacity region is a superset (subset) of the capacity region of the original network. This paper derives bounding models from noiseless links, with lower bounding models corresponding to points in the channel's capacity region and upper bounding models corresponding to points in a new channel characterization called an emulation region. Replacing all channels in a network by their noiseless upper (lower) bounding models yields a network of lossless links whose capacity region is a superset (subset) of the capacity region for the original network. This converts a general (often stochastic) network into a network coding instance, enabling the application of tools and results derived in that domain. A channel's upper and lower bounding models differ when the channel can carry more information in some networks than in others. Bounding the difference between upper and lower bounding models bounds both the accuracy of the technique and the price of separating source-network coding from channel coding.
机译：引入了一种限制独立信道网络容量的技术。第一部分和第二部分分别处理点对点和多终端通道。使用称为边界模型的新工具导出边界。如果在任何网络中用信道1替换信道2会产生一个新网络，其容量区域是原始网络容量区域的超集（子集），则信道1是信道2的上限（下限）模型。本文从无噪声链接中得出边界模型，其下边界模型对应于信道容量区域中的点，而上边界模型对应于新信道特征（称为仿真区域）中的点。用其无噪声的上（下）边界模型替换网络中的所有通道，将产生一个无损链路网络，其容量区域是原始网络容量区域的超集（子集）。这样可以将通用（通常是随机的）网络转换为网络编码实例，从而可以应用该域中衍生的工具和结果。当通道在某些网络中可以承载比其他网络更多的信息时，通道的上限和下限模型有所不同。限制上下边界模型之间的差异不仅限制了该技术的准确性，而且也限制了将源网络编码与信道编码分离的代价。

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