This same question was posted to the PicBasic forums a couple of days ago. That post indicated that an RF link is part of the scenario.
I pointed that poster to an example posted by Bruce Reynolds showing how to decode a Holtek HT640 which uses a similar approach although with different details for "0", "1" and "f".
The simplest method is to wait for the long space at the end of the first transmitted copy and then use the CCP hardware to capture the pulses and spaces of the second transmitted copy.