Capacity of a class of tree networks

In this paper, we characterize the capacity of a class of single-source single-destination discrete memoryless relay networks with an arbitrary number of nodes. In this class, the network is assumed to have a tree topology where the root node is the source, each parent node in the graph has at most one noisy child node and any number of noiseless child nodes, and the set of leaf nodes is the destination. A combination of decode-and-forward (DF) and compress-and-forward (CF) at noisy relay nodes is shown to be optimal. Our result is the first to show that the combination of DF and CF is capacity achieving for a non-trivial class of noisy networks with an arbitrary number of nodes.