IR diode radiation spot area
The simplistic approach that you show will not work for almost any distance between the devices. You will need to apply some more technology to have any chance of getting anything to work similar to what you envision. 

For close proximity where you align the transmitter physically close to the receiver you may be able to get this to work by adding an isolating tunnel around and in front of each receiver IR diode. This would effectively let each receiver just see what is directly in front of it in a narrow spot.

If you envision something that you want to use over an appreciable distance then you are going to have to resort to a special modulation protocol that allocates a certain part of the protocol to each of your channels. This can take many forms depending upon how much effort you want to invest in the design. One approach would be to devise a transmit protocol divided up into N time slots with a distinguishing  frame syncing to identify when the channel slot sequence starts. A decoder circuit or MCU behind each receiver looks for its specific time slot to strip its specific data out. In this scheme you could drive all your transmitter IR LEDs in parallel (or just use one).