The sum-rate capacity of general degraded interference networks with arbitrary topologies

In this paper, a full characterization of the sum-rate capacity is established for the general degraded single-hop communication networks with any arbitrary topology. It is proved that a successive decoding scheme is sum-rate optimal for these networks. Also, it is shown that the transmission of only a certain subset of messages is sufficient to achieve the sum-rate capacity in such networks. An algorithm is presented to determine this subset of messages explicitly. This algorithm is described using novel graphical illustrations. The sum-rate expression for the degraded networks is then used to derive a unified outer bound on the sum-rate capacity of arbitrary non-degraded networks. Some variations of the degraded networks are given for which the derived outer bound is sum-rate optimal. Specifically, for the first time, network scenarios are identified where the incorporation of both successive decoding and treating interference as noise achieves their sum-rate capacity.