The issue is, you deal with the system you're with, not the situation you wish you had.
We can't change a transmission protocol or route data over arbitrary connections. This is a collection of everything from very old hardware to brand new, protocols from very old to brand new, in every country in the world, and you can't just arbitrarily rework them. It's the same in the air, too. And when new protocols are made, they're generally in addition to existing ones, not replacing them. I'm not aware of any with error correcting codes or the like (there could be, I just haven't worked with them), but some of them (not all) use checksums (though that's a whole 'nother story... the documentation on how one common type of checksum, that used in datalink messages, is a big fat lie, caused by a screwup in whoever implmented the code the first time that everyone else now has to imitate... but it works, so...).
In the long run, the goal is to move as much traffic as possible to the more automated, more reliable newer protocols. But this is something that's invariably going to happen at a snail's pace.
As I've never messed with them directly, I can't decribe to you the protocols used for physical data transmission at every point over the FARICE and DANICE links - just the message layer on top of them, which is plaintext except for the header marker characters. I've never worked at anything more than the endpoints. But I can tell you this, there's no way we could just go in and replace all of the hardware along the way (you should see the graph of all of the hardware that exists just between Iceland and Britain). It would be an expensive long-term international effort with major potential for disruption in its own right. And it would only help for that particular link anyway. What you really want is how all of air traffic control messages are transmitted - aircraft, atc, tower, etc - everywhere in the world to be switched over to a single, reliable mechanism and a standardized set of international routing hardware. Well, great, join the club, I'd love that too! But it's just not going to happen any time soon without a massive funding surge.
You work with the systems that you have, not the systems you wish you had. Yes, we're working to modernize everything, just like everyone else. For example, in the past year I've spent a good bit of time working on adding in capabilities to one system to help take a sort of "middleman" server that it talks to out of the loop to improve reliability and error logging. But these things don't happen fast. And how many programmers / hardware engineers do you think we have, really? We're no Microsoft here.