What we do know is that they produce a variety of signals, some very complex and their communication is super fast, which is another obstacle for possible "communication". For example, we cannot generate a burst pulse with our current technology, we can only record theirs and play it back.
But many research groups are trying. We are starting Dolphin Chat citizen science project on Zooniverse in a month or so, to classify and prepare a large dataset of bottlenose dolphins' vocalizations for out deep learning model. You can check it out and even participate, it will definitely help to appreciate how complex their vocal repertoire is (and how "chatty" they are).
The burst pulse is extremely complex, some can have 400 single clicks in one pulse (our ear cannot even hear these single pulses, they merge and for our human ear it sounds like a creaky door), and the pulse duration is like a few seconds. Each click is broadband (can go up to 100 kHz and beyond), it is frequency modulated with varied peak frequencies, center frequencies, RMS, some clicks can have 2 peaks, etc. It is super fast and super complex, we we cannot just generate one, only dolphin's sound producing mechanism can.
It is not active yet, it will be in a month or so. You can also sign up for our newsletter here: cetalingua.com , we will send notification when this project goes live.
He basically found that dolphins language follow the Zipf law and Shannon information theory.
Baby dolphins also have a babbling periode like humans in the same timespan. It is interesting talk all the way through. Maybe you can contact him.
https://youtu.be/H30NipTkA5s https://simple.m.wikipedia.org/wiki/Zipf%27s_law
Does anyone have the sea world connections to make that happen?