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.

中文翻译：

---

机会拓扑干扰管理

拓扑干扰管理 (TIM) 问题研究部分连接干扰网络的自由度 (DoF)，除了网络拓扑（即部分连接）之外，在发射机上没有信道状态信息 (CSI)。在本文中，我们考虑具有网络拓扑不确定性的 TIM 问题的变体，其中具有部分连通性的信道状态只知道属于 百万美元 发射器的状态。特别是，发射机可以通过以下方式访问所有网络拓扑信息 百万美元 状态，但不知道它究竟属于哪个状态进行通信。除了所有状态的网络拓扑之外，任何状态的接收器都知道它所处的确切状态，并希望尽可能多地恢复当前状态下的高优先级信息。我们将其表述为具有网络不确定性的机会主义 TIM 问题 百万美元 状态变化的网络拓扑。为了适应网络拓扑的不确定性和不同的消息解码优先级，分别在发送端和接收端启用联合编码和机会解码。具体来说，在了解所有可能的网络拓扑结构后，每个发射器都会发送一个信号，该信号由所有所需的消息联合编码 百万美元 州，说 百万美元 不同的消息，并且在某个状态 百万美元 ， 接收者 $千$ 希望机会性地解码第一个 $\pi _{k}(m) \in \{1,2,\cdots,M\}$ 更高优先级的消息。在这种机会主义的 TIM 设置下，我们构建了一个多状态冲突图来捕获消息的相互冲突 百万美元 状态，并通过多面体组合来表征两类网络拓扑的最佳 DoF 区域。一个值得注意的事实是，在额外的温和单调条件下，正交接入和一对一干扰对齐的最优条件仍然适用于网络拓扑不确定的TIM。