Faster-than-light communication (or what Star Trek calls "subspace" communication) is theoretically possible within the constraints of general relativity. In a particular inertial frame of reference A, GR allows an object surrounded by curved spacetime (spacetime curved within within A) to have a velocity greater than c w/respect to time in A.

Such a reference frame was modeled in Alcubierre's 1994 paper, and NASA is even working on warp drives that where the distortion required (or the negative energy associated with the distortion) is significantly lower than what is described in the Alcubierre metric. . .

NASA Actually Working on Faster-than-Light Warp Drive |

FTL communication can be made to work on the same principle; instead of encasing a large object like a ship in a "warp bubble", wrap the warp bubble around photons--which we know behaves exactly the same as matter in GR. It's expected that the negative energy to create such a bubble around photons would be tremendously small compared to what would be required for a ship since a photon's "mass" (as measured by the distortion it causes to the spacetime around it) as given by h/(photon's wavelength * c) is tremendously small compared to that of a ship.

Of course, to make it practical, a big assumption needs to be made--that no energy is required to maintain the photon's warp bubble from the time the photon acquires it (at the transmitter) until it reaches its destination (at the receiver).