Zero-error network coding for acyclic networks

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 Γ_N^* and Γ~_N^*, 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.