Generalized Degrees of Freedom of the Symmetric $K$ User Interference Channel Under Finite Precision CSIT

The generalized degrees of freedom (GDoF) characterization of the symmetric K user interference channel is obtained under finite precision channel state information at the transmitters (CSIT). The symmetric setting is where each cross channel is capable of carrying α DoF, while each direct channel is capable of carrying 1 DoF. Remarkably, under finite precision CSIT the symmetric K user interference channel loses all the GDoF benefits of interference alignment. The GDoF per user diminish with the number of users everywhere except in the very strong (optimal for every receiver to decode all messages) and very weak (optimal to treat all interference as noise) interference regimes. The result stands in sharp contrast to prior work on the symmetric setting under perfect CSIT, where the GDoF per user remain undiminished due to interference alignment. The result also stands in contrast to prior work on a subclass of asymmetric settings under finite precision CSIT, i.e., the topological interference management problem, where interference alignment plays a crucial role and provides substantial GDoF benefits.