SYNTHESIS OF PROBABILISTIC COMMUNICATION NETS

In this thesis the necessary and sufficient conditions for an expected value terminal capacity matrix to be realized as a net with a tree structure are developed. There are two reasons for the constraint that the net have a tree structure. First, it is well known in the classical communication synthesis problem that if a realization exists, then a realization with a tree structure always exists. Secondly, since the path between two vertices in a tree is unique Fu's equation for computing the expected value terminal capacity for these vertices reduces to a simple form. The expected value terminal capacity for vertices i and j in a tree net is the product of the edge probabilities in the path between vertices i and j multiplied by the edge weight which has the minimum value in that path. (Author)