Class Response: Radio censorship

This week during our discussion about radio, the FCC was brought up. Mr. Miller spoke about how, because radio is public and accessible to everyone, it must be censored in some respects. As discussed, the FCC, or Federal Communications Commission, is a part of the government. Upon hearing this I immediately questioned its' possible violation of the first amendment; freedom of speech and of the press in particular. I brought this up in class and received the explanation that, because it's public, this is allowed. Also, the radio must be monitored in terms of how it is divided and the rights that go along with it. But I still feel like it is a bit off.
I understand that people don't want to turn on the radio and hear a bunch of vulgarity, but what separates indecency from expression? I feel as though, because radio stations are either independent or under an organized conglomerate, it should be up to the discretion of their leaders to decide what their policies are. Perhaps such policies themselves could be monitored, and if the stations violate anything laid out in their agreements an intervention of the FCC could justifiably take place.
I sincerely believe that radio should have the same rights applied to it as any of form of media, as stated in the constitution. There are no regulations of literature. Anyone can write anything and publish it, and by publishing it it becomes public. If stations were notoriously profane, people could simply not tune in. They could, instead, listen to a station that has agreed to be clean. There could even be a rating system similar to that of movies that could be broadcasted periodically. For example, every hour or so the stations would be obligation to make a statement such as, "Please note that 98.9 DJX is a 'R' station; listener discretion advised."
I do not know much about this topic, and am probably too under-educated to make this statement. But logically, I don't see much argument against it. Just because 50 Shades of Gray was published doesn't mean that everyone is subjected to reading it. However, radio is a cool media and requires less intention for people to consume it. A really dirty song could come on and a person could unknowably have its station on. But does this mean that profanity shouldn't be allowed? In my opinion, it doesn't.