How To Make Messages Easy For an Alien Race To Understand (hackaday.com)
szczys writes: The screen on that new cellphone has amazing pixel density, color vibrance, and refresh rate. The high-end headphones you just picked up do an amazing job reproducing sound. These devices interface extremely well with humans but might not be very good modes of communication for an Extra-Terrestrial Intelligence. Sure, we haven't made contact with alien life yet. Even if they did pick up our broadcasts or space probes the relatively narrow-range of audio (narrow and low frequency), visual (slow refresh rate), and data transmission methods are likely to make no sense to non-human entities. The Voyager Golden Record took a fascinating approach to making some data available to new civilizations; it's interesting to think of other ways we might communicate with beings of fundamentally different biology.
Don't bother. If they have the ability to pick up the signal, they'll have the ability to decipher the message.
Read LINCOS: Design of a Language for Cosmic Intercourse, Part 1 by Hans Freudenthal, North Holland Publ. 1960. Unfortunately, he never got to publish the second volume covering more advanced concepts, but the language was further developed by NASA and by various enthusiasts later. It's still the most systematic treatment for communicating with aliens.
This is 'sci-fi' optimism. You assume that warp drives and hyperspace will eventually trickle down into reality. Our current understanding of physics doesn't make FTL travel for matter look very promising, and we've yet to detect anything that does. Even before humans broke the sound barrier, we observed things that did so all the time. Just like we knew heavier-than-air flight was possible, because birds exist.