On the Optimality of Treating Interference as Noise: General Message Sets Revisited

We study the optimality of power control and treating interference as noise (TIN) in the M × N X channel, from the generalized degrees-of-freedom (GDoF) and constant- gap capacity perspectives. A result by Geng, Sun and Jafar shows that if there exist K = min(M, N) transmitter-receiver pairs such that each direct link strength is no less than the sum of the strongest incoming and strongest outgoing cross link strengths (all in dB), then it is optimal to reduce the M × N X channel to a K-user interference channel and use TIN. The proof of this result relies on a deterministic approximation of the original Gaussian network, specifically for the case M <; N. Here we present a simpler proof by working directly with the original Gaussian network. Our proof relies on a new "less noisy under interference" order exhibited by TIN-optimal M × N X channels, akin to the "less noisy" order in broadcast channels.