Cut-set bound for multimessage multicast networks with independent channels and zero-delay edges

We consider a communication network consisting of nodes and directed edges that connect the nodes. Each edge receives a symbol from a node and outputs a symbol to a node in each time slot. An edge (ℓ, i) terminating at node i is said to incur zero delay on an edge (i, j) originating from node i if the following holds in each time slot: Node i receives the symbol output from (ℓ, i) before encoding the symbol to be transmitted on (i, j). Otherwise, (ℓ, i) is said to incur a delay on (i, j). In the classical model, every edge incurs a unit delay on every other edge and the cut-set bound is a well-known outer bound on the capacity region. However, if an edge is allowed to incur zero delay on another edge, then there exists a two-node network whose capacity region exceeds the classical cut-set bound. In this paper, we investigate the multimessage multicast network (MMN) consisting of independent channels and study the capacity region under an edge-delay model where an edge may incur zero delay on some other edges. Our edge-delay model subsumes the classical model. 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 classical unit-delay assumption.