Looking around the Internet for some additional information about IR transmission, I found out that i.e. SONY uses a Pulse Width Modulation protocol that looks simple to implement with PICs (http://www.sbprojects.com/knowledge/ir/sirc.htm).

So instead of trying to establish a "serial" communication, I'll have a go with PULSOUT/PULSIN.

Might be easier since the IR (hardware) layer is already working well.