Beyond network equivalence

In earlier work, we described an equivalence result for network capacity. Roughly, that result is as follows. Given a network of noisy, memoryless, point-to-point channels, replace each channel by a noiseless, memoryless bit pipe of the same capacity yields a new network such that any collection of demands can be met on the network of noisy links if and only if the same demands can be met on the network of noiseless links. We here expand on these ideas to provide a framework for studying more general networks, including networks containing memoryless broadcast, multiple access, and interference channels. For each network in this broader class, we design two corresponding networks of noiseless, memoryless point-to-point links. These two networks provide upper and lower bounds in the following sense. Fix an arbitrary collection of demands. If the given demands can be met on the lower bounding network, then they can also be met on the original network. Likewise, if the given demands can be met on the original network, then they can also be met on the upper bounding network.