Is it possible to send commands to an EV3 brick from the Power Functions Speed Control remote?
Would I have to interpret the raw sensor values to do this? Are there any references that would help?
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It is possible, but not with the LEGO EV3 IR Sensor.
The LEGO 45509 EV3 Infrared Sensor does not respond to the 8879 remote. There is actually a "hidden" mode that is not accessible from the standard LEGO software called IR-REM-A that is essentially this "raw" mode that you have conjectured. However even in this mode, it does not respond to the 8879 remote (unless you press both brake buttons at the same time, which is not very useful).
Instead, you could use the HiTechnic IR Receiver sensor which does work with the 8879 remote. There is not an EV3 block for it, so you will need to use a 3rd party development platform that supports it, such as ev3dev.
Or, you could also use LIRC. There are lots of options for IR Receivers included homebrew (if you are a hardware hacker). Although not exactly what you need, here is an example of someone who make an IR Transmitter for the EV3 to control Power Functions motors (using ev3dev).