On the Equivalence of Shannon Capacity and Stable Capacity in Networks With Memoryless Channels
An equivalence result is established between the Shannon capacity and the stable capacity of communication networks. Given a discrete-time network with memoryless, time-invariant, discrete-output channels, it is proved that the Shannon capacity equals the stable capacity. The results treat general demands (e.g., multiple unicast demands) and apply even when neither the Shannon capacity nor the stable capacity is known for the given demands. The result also generalize from discrete-alphabet channels to Gaussian channels. Shannon's information theory provides a fundamental framework for studying network communications. Under this paradigm, the sources are assumed to be saturated, and thus the source nodes can rely on long vectors of source symbols that are available before encoding begins, and receivers decode complete messages after all channel outputs are received.