I'm going to go off on a tangent here and pretend your question was: "I have come up with this encryption which I think is cool and I wrapped it in the following story. Is it ready for puzzling.se? If not, what does it need?"
I believe the frame needs work in order to set expectations. I took a look at the puzzle and here's What I Have Tried.
On the one hand the radio operator and di di da suggests Morse code. On the other hand the emphasis on afar and weak signal suggests it didn't originate on Earth and hence isn't Morse or even an English message. If the receiver is a radio operator, wouldn't he recognize Morse? If the sender knew Morse, wouldn't he or she know to put in spaces?
Three branches occur to me at this point:
- It's an alien message and the most likely solution is to reformat it as a picture or pattern as that's how they would probably communicate to another culture.
- It's Morse without spaces suggesting an Earth-derived source at some distance that wants to obscure the message for some reason.
- It's some other encryption and the radio di da (wasn't there a Queen song about that?) is a red herring.
The obvious choices for 3 would be a hex or octal encoding of ASCII but there are several long runs of 0s and 1s which are outside the printable range so this is unlikely. Other encryption choices are certainly possible. On the other hand since the question is "where did they come from" it could be an encoding of celestial or galactic co-ordinates or positional information of some kind. Maybe afar isn't as far as space and it's latitude and longitude or GPS. How reliable is the narrator's gut? Several possibilities here but I'm inclined to put this aside.
There is a very small amount of information to make a picture (hats off to Gareth for a good try) so I would consider 1 unlikely as well.
How does 2 look? Well, I don't know if 0 is a dot or a dash. A quick look at the Morse table says that if this is straight-ahead Morse the first letter is E, F, I, or U if 0 is a dot or G, M, Q, or T if 0 is a dash. Each of these eight possibilities has about four possibilities for the second letter. Each of those has four possibilities for the next letter and so on. This quickly becomes unmanageable unless I can somehow prune the search tree.
I paused at this point to do a little meta-analysis. If I translated a normal message into Morse and took out the spaces, would that be cool enough? Probably not. Probably the poster at a minimum would begin the message with "QRT7 calling Earth...". The message might be in Caesar cipher. How do I know when to prune? If the signal is noisy, could some digits be wrong or missing? Also, I am by no means certain that Morse is really the first step. This could be a total waste of time.
This is why I think the puzzle is not yet ready. I am facing a lot of work chasing a lot of paths with no way of knowing whether or not I am on the right track. My reward is uncertain: why should I even be interested in this message? I cannot gauge my progress. The work to reward ratio doesn't appeal to me.
What would make it better? What if the receiver was a post-apocalyptic survivor who recognized the message as being from one of the spacecraft they used to send up in ages past? What message from a former civilization is it trying to send? This gives us motivation to solve it and you can set expectations for the solution. Maybe previous messages were words, pictures, formulas... whatever. Something to save me from expending arbitrary amounts of effort following random paths for an uncertain reward.
I hope this helps. I would really like to see you turn this into an enjoyable puzzle.