Communicating over large distances is basically out of the question with modern technology - you will always be limited to the speed of light. Of course, we can still consider other alternatives.

Tachyons are a good option, and are always popular in science fiction. Just as we can't travel faster than the speed of light, tachyons can't travel slower than the speed of light. So, getting them to travel at high speeds is no problem. They do it automatically. The only real problem is that tachyons are purely theoretical, and there is absolutely no evidence of their existence.

The other option, has to do with "linked" particles. I've only heard of it once or twice, and so I really can't explain it much. Maybe someone here can say better than I. Some how, to particles can be created that are "linked" together, and anything that changes the state of one changes the state of the other (supposedly) instantly, and independently of distance. But, I don't know too much about, so that's about all I can say.