What is your communication based on?
Electromagnetic radiation (Light, radio, infrared, ultraviolet into gammas - light speed limit, either drop off as the square of the distance (omnidirectional) or are aimed at a very limited area in the sky (collimated, coherent, laser/maser) and can be jammed mainly by overwhelming the signal - theoretically by absorbing it, if you know the wavelength,
Neutrinos - there has to be a better way than thousands of litres of dry cleaning fluid at the bottom of a gold mine for detecting neutrinos, second-hand trinos or even worn out trinos. Anyway, they're restricted to light speed (except on Italian autostrada) and omnidirectional, and generated at random by stars, so not very long range.
Gravity waves - can't be blocked, would love to make coherent gravity waves. Some mathematical physicists believe they travel considerably faster than light, which would severely damage special relativity. We don't have any measuring implements precise enough to test this, though, let alone any way of generating test signals. A pair of tiny black holes rotating fast enough (MHz at least) round their mutual centre of gravity to overcome their mutual attraction?
Wormholes - through which we pump photons. The two ends of a wormhole - or one end, seem from a different perspective - are no distance from each other, even if one is light years away. If the wormhole is not on the surface of a planet - and it seems a bit tough allowing for all the relative velocities involved, putting it into a metal box should stop the energy getting any further. Obviously, if other than photons are used, the means of enclosure might need to change.
Quantum entanglement - Associative magic - things that once came into contact maintain a mutual influence until the end of time. Tickle one of them, and the other, wherever it might be in the cosmos, giggles. This is seriously worrying to relativity, which has no sense of humour. And at the beginning, close to the big bang, just about everything was in contact with everything else, although I suppose we can wait until particles crystallise out , so only a percentage of matter would be in communication. Very difficult to find a way of blocking this. Delay time unknown, possibly zero.
Hyperwave - If an equivalent to electromagnetic radiation can propagate in a universe with either a smaller diameter or a much higher maximum speed limit then I don't know how to stop it.
Ansible - See how much neater fiction is than physics. No way of screening against it - kill the operator, take a sledgehammer to the device. What, there are hundreds of thousands of the gadgets? You'd better get going then, haven't you?