Opportunistic Treating Interference as Noise

We consider a $K$-user interference network with $M$ states, where each transmitter has $M$ messages and over State $m$, Receiver $k$ wishes to decode the first $\pi_k(m) \in \{1,2,\cdots,M\}$ messages from its desired transmitter. This problem of channel with states models opportunistic communications, where more messages are sent for better channel states. The first message from each transmitter has the highest priority as it is required to be decoded regardless of the state of the receiver; the second message is opportunistically decoded if the state allows a receiver to decode 2 messages; and the $M$-th message has the lowest priority as it is decoded if and only if the receiver wishes to decode all $M$ messages. For this interference network with states, we show that if any possible combination of the channel states satisfies a condition under which power control and treating interference as noise (TIN) are sufficient to achieve the entire generalized degrees of freedom (GDoF) region of this channel state by itself, then a simple layered superposition encoding scheme with power control and a successive decoding scheme with TIN achieves the entire GDoF region of the network with $M$ states for all $KM$ messages.