I'm still having trouble with getting the right signal, even when the cables aren't connected to anything I still get signals with about 20000 of microseconds time between them. How should I connect the arduino to my transmitter in a way that there is a common ground?
I can't answer your question without more details about the transmitter's ppm signal output. The ground would simply wire to a arduino ground pin, that should not be an issue. But we lack info on the PPM signal itself. Is it a 0 to +5vdc signal or 0 to battery voltage signal? What is the logic of the PPM signal, that is, is a HIGH a bit on condition (true logic) or is a LOW a bit on condition (negative logic)?
These things have to be known before proper electrical interfacing can be performed and before your software can properly decode the data stream. Making assumptions on these things makes debugging between hardware and software bugs or possible both a difficult task.
If I was taking on such a project, I would first get out my old analog scope and check out the PPM signal until I fully understood it's properties.
Good luck;
Lefty