Is it possible to encrypt an audio wave? NFL Example
Someone mentioned how occasionally, these radios will pick up interference from airplanes, and that frequently the helmets lose communication.


Is this the 1970s?

Modern headsets should be pretty robust against interference, and they have a dedicated spectrum allocation. If there's interference from airplanes, either device malfunctions.

So, no, this sounds like rumors, or long obsolete claims, especially since for superposition reasons and 6 decades of compatibility, aircraft voice comms is partly still AM; modern (as in: post-1970) headsets are either digital or at the very least FM.


  One thing I wonder about is if an opposing team's coaches could pick up what was being communicated between the offensive coordinator and the quarterback.


Sure. It's on the air. Radio waves can't tell friend from foe. And since a quarterback can be all over the field, there's certainly no high-gain antenna focusing the radio beam on the player alone.


  And then I wonder, well, why wouldn't there just be an encryption scheme between the coach and the quarterback.


Just because you can receive the mobile phone call of your neighbor, or his WiFi, or pay TV, doesn't mean you can decrypt stuff.

So, yes, there's plenty encryption systems in the technological fields of voice comms, some civil, some military... plenty to pick from.


  But then I wonder if the encrypted signal would be distorted with all this noise, and if that distortion would completely disrupt the decrypted signal.


Digitally, whether or not the signal is encrypted makes little difference to the signal quality in case of errors. You typically break one full "frame" worth of channel coding / encryption.

All wireless digital communication schemes incorporate channel coding that allows for forward error correction (FEC) so that this makes no difference, and the audio codecs (specifically: the VoCoder) for such communication channels are robust against "surviving" errors.


  Are there any methods for this kind of "loose encryption"?


I'll not go into crypto here, because a) that's not my forte and b) because this isn't the perfect platform, but:

No, that's something a cryptographer must never implement; every encryption must have zero correlation between encrypted and decrypted bits. If that wasn't the case, the cryptography would be inherently insecure, because you could, through statistics, relatively easily reconstruct (parts of) the unencrypted communication.

There are "human" encryption schemes. Like NFL coaches could change the name of their plays from game to game. This would keep it known to only the QB and the coach.


  There are "human" encryption schemes. Like NFL coaches could change the name of their plays from game to game. This would keep it known to only the QB and the coach.


That would be called a "substitution cipher", and these are extremely weak. Especially, you call a specific move "rabbit", and then the quarterback does a move, for the rest of the game it's clear what "rabbit" means.

Commentary on the situation: Obviously, the solution to this problem is organizational, not technological: It's a sport. If you cheat, you get disqualified. So, there's strong incentive not to take performance-enhancing drugs. And there's just as much incentive to not use information you mustn't get. 

Just that the supervision of the former requires invasive, expensive testing, and the question what kind of knowledge a coach had can be relatively easy tested within similar margins of error as drug tests with basic statistics.