Opportunistic topological interference management

The topological interference management (TIM) problem studies the degrees of freedom (DoF) of partially-connected interference networks with no channel state information (CSI) at the transmitters except the network topology (i.e., partial connectivity). In this paper, we consider a variant of the TIM problem with uncertainty in network topology, where the channel state with partial connectivity is only known to belong to one of $M$ states at the transmitters. In particular, the transmitter has access to all network topological information over $M$ states, but is unaware of which state it falls in exactly for communication. The receiver at any state is aware of the exact state it falls in besides the network topologies of all states, and wish to recover as much highly-prioritized information at current state as possible. We formulate it as the opportunistic TIM problem with network uncertainty modeled by $M$ state-varying network topologies. To adapt to network topology uncertainty and different message decoding priority, joint encoding and opportunistic decoding are enabled at the transmitters and receivers respectively. Specifically, being aware of all possible network topologies, each transmitter sends a signal jointly encoded from all messages desired over $M$ states, say $M$ distinct messages, and at a certain State $m$, Receiver $k$ wishes to opportunistically decode the first $\pi_k(m) \in \{1,2,\cdots,M\}$ higher-priority messages. Under this opportunistic TIM setting, we construct a multi-state conflict graph to capture the mutual conflict of messages over $M$ states, and characterize the optimal DoF region of two classes of network topologies via polyhedral combinatorics. A remarkable fact is that, under an additional mild monotonous condition, the optimality conditions of orthogonal access and one-to-one interference alignment still apply to TIM with uncertainty in network topology