网络等价理论第一部分与II
A Theory of Network Equivalence, Parts I and II
摘要：
介绍了一种用于网络容量定界的等价工具族。第一部分讨论点对点通道网络。主要结果大致如下。给定一个有噪声的、独立的、无记忆的点对点信道的网络，当且仅当在另一个网络上可以满足通信需求的集合时，才可以在给定的网络上满足该集合，在该另一个网络中，每个有噪声的信道被具有等于有噪声的信道容量的吞吐量的无噪声比特管道代替。这个结果是已知的单源组播需求的情况下，以前。这里给出的结果处理一般需求-包括，例如，多个单播需求-并且即使在无噪声网络中对应需求的可实现速率区域未知时也适用。在第二部分中，一般渠道的上限和下限渠道模型的定义。通过这些定义，一组通信需求可以在一个独立信道的网络上得到满足，如果它可以在一个网络上得到满足，其中每个信道被其下界模型所取代，并且只有当它可以在一个网络上得到满足，其中每个信道被其上界模型所取代。这项工作得出的一般条件下，网络的无噪声位管道是一个上限或下限模型的多端通道。给出了用于广播、多址和干扰信道的示例上边界和下边界模型。然后，它示出，边界的上限和下限模型之间的差异，对于一个给定的信道收益率的准确性上的界限，使用这些模型得出的网络容量界限。通过由无噪声比特管道的网络的网络编码容量来限制独立噪声信道的网络的容量，该方法表示朝向构建用于限制网络容量的计算工具的目标的一步。
英文摘要：
A family of equivalence tools for bounding network capacities is introduced. Part I treats networks of point-to-point channels. The main result is roughly as follows. Given a network of noisy, independent, memoryless point-to-point channels, a collection of communication demands can be met on the given network if and only if it can be met on another network where each noisy channel is replaced by a noiseless bit pipe with throughput equal to the noisy channel capacity. This result was known previously for the case of a single-source multicast demand. The result given here treats general demands -- including, for example, multiple unicast demands -- and applies even when the achievable rate region for the corresponding demands is unknown in the noiseless network. In part II, definitions of upper and lower bounding channel models for general channels are introduced. By these definitions, a collection of communication demands can be met on a network of independent channels if it can be met on a network where each channel is replaced by its lower bounding model andonly if it can be met on a network where each channel is replaced by its upper bounding model. This work derives general conditions under which a network of noiseless bit pipes is an upper or lower bounding model for a multiterminal channel. Example upper and lower bounding models for broadcast, multiple access, and interference channels are given. It is then shown that bounding the difference between the upper and lower bounding models for a given channel yields bounds on the accuracy of network capacity bounds derived using those models. By bounding the capacity of a network of independent noisy channels by the network coding capacity of a network of noiseless bit pipes, this approach represents one step towards the goal of building computational tools for bounding network capacities.
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