We consider a communication network consisting of nodes and directed edges that connect the nodes. The network may contain cycles. The communications are slotted where the duration of each time slot is equal to the maximum propagation delay experienced by the edges. The edges with negligible delays are allowed to be operated before the other edges in each time slot. For any pair of adjacent edges @math and @math , where @math terminates at node @math and @math originates from node @math , we say @math incurs zero delay on @math if @math is operated before @math ; otherwise, we say @math incurs a unit delay on @math . In the classical model, every edge incurs a unit delay on every adjacent edge and the cut-set bound is a well-known outer bound on the capacity region. In this paper, we investigate the multimessage multicast network (MMN) consisting of independent channels, where each channel is associated with a set of edges and each edge may incur zero delay on some other edges. Our result reveals that the capacity region of the MMN with independent channels and zero-delay edges lies within the classical cut-set bound despite a violation of the unit-delay assumption.
This paper investigates the impact of noise dependence and signal delay on the capacities of networks. It is shown that statistical dependence between the noise in a network's component channels is helpful for communication. In particular, the capacity region of a network whose component channels exhibit dependent noise is a superset of the capacity region of a network built from the same component channels when the noise in those channels is independent. It is also shown that delay has no impact on capacity. That is, the capacity of a network of memoryless channels is unchanged by the addition of finite delays anywhere in the network. Both results are proven for all possible networks of memoryless point-to-point and multi-terminal channels under multiple multicast connections. All other connection types (e.g., single unicast, multiple unicast, single multicast, and mixed unicast and multicast connections) are special cases of the multiple multicast problem, and are therefore included in the given results. The results also generalize from reliable communication of independent sources to lossy or lossy description of possibly dependent sources (i.e., joint source-channel coding) across the same network.