Two-user interference channels with local views: On capacity regions of TDM-dominating policies

We study the limits of reliable communication in two-user interference channels where each of the two transmitters knows a different subset of the four channel gains characterizing the network state. In order to systematically analyze this problem, we introduce two concepts. First, we define a local view model for network state information at each transmitter, wherein each transmitter knows only a subset of the four channel gains. This subset may be mismatched from that of the other transmitter, limiting the ability of the two transmitters to coordinate transmission decisions. Second, we define a notion of maximal rate regions achievable by transmission policies that dominate time-division multiplexing (TDM). Specifically, these 'TDM-dominating capacity regions' characterize rates achievable when transmission schemes must, for every possible realization of network state, achieve rates at least as good as what can be achieved through TDM. We consider a set of seven symmetric local views based on an assumption that each transmitter uses the same mechanism to gather its local view. For five out of the seven local views, we show that TDM is sufficient to achieve the full TDM-dominating capacity region for the linear deterministic interference channel. For these five local views, our result implies that no single policy can achieve a rate point outside the TDM region without inducing sub-TDM performance in another network state. The common traits shared by the two remaining local views (those with better performance than TDM) are: first, each transmitter knows its outgoing interference channel gain, and second, there exists at least one channel gain known to both transmitters. For these two local views, transmitters can use their knowledge to achieve opportunistic rate gains beyond TDM. Using the relationship between the linear deterministic channel and the Gaussian channel, we extend our conclusions to bounded gap characterizations of the TDM-dominating capacity region for the Gaussian interference channel with local views.