It's unlikely for evolution to produce such a communication mechanism as it involves non-local refactorings. Under that constraint, and assuming efficiency is selected for, they will reserve shorter symbols for more common concepts and end up with something like Zipf's Law (but again, not a global optimum).
Now, if they were intelligent, they would (as we do) come up with highly compressed encoding schemes that would have no apparent patterns to an outsider, except perhaps control signals at the start and end. But if they wanted to be heard by aliens, they would avoid using obscuring mechanisms like compression.
What if they were smart enough to see that contacting aliens wasn't in their best interests? What if they understood that continually seeking to harness ever more energy was ultimately futile and just decided to enjoy their existence without disturbing others or being known to anyone else?
Someone read Douglas Adams?
(if not, you probably should)
Anyway, I would argue, that wanting to allways remain in the same state of being, is not very smart, since the enviroment is going to change anyway ... so you got to evolve to adopt to new enviroment changes (ultimately the collapying of our sun)
A big part of human communication, especially spoken communication, is redundant, to allow error correction. Repetition and redundant context clues allow us to reconstruct meaning from lossy signals; language is a funny balancing act between compression and interpretability.
Now, if they were intelligent, they would (as we do) come up with highly compressed encoding schemes that would have no apparent patterns to an outsider, except perhaps control signals at the start and end. But if they wanted to be heard by aliens, they would avoid using obscuring mechanisms like compression.