In this paper, we consider a point-to-point communication network of discrete memoryless channels. In the network, there are a source node and possibly more than one sink node. Information is generated at the source node and is multicast to each sink node. We allow a node to encode its received information before loading it onto an outgoing channel, where the channels are independent of each other. We also allow the nodes to pass along messages asynchronously. In this paper, we characterize the admissibility of single-source multi-sink communication networks. Our result can be regarded as a network generalization of Shannon's result that feedback does not increase the capacity of a discrete memoryless channels (DMCs), and it implies a separation theorem for network coding and channel coding in such a communication network.

Consider transmitting a set of information sources through a communication network that consists of a number of nodes. Between certain pair of nodes, there exist communication channels on which information can be transmitted. At a node, one or more information sources may be generated, and each of them is multicast to a set of destination nodes on the network. In this paper, we study the problem of under what conditions a set of mutually independent information sources can be faithfully transmitted through a communication network, for which the connectivity among the nodes and the multicast requirements of the source information are arbitrary except that the connectivity does not form directed cycles. We obtain inner and outer bounds on the zero-error admissible coding rate region in term of the regions /spl Gamma//sub N//sup */ and /spl Gamma/~/sub N//sup */, which are fundamental regions in the entropy space defined by Yeung. The results in this paper can be regarded as zero-error network coding theorems for acyclic communication networks.