After spending more time with my adapted 16x16 LED board (made with four 8x8 red dot LED matrices - as shown in Part 1), I added an IR receiver module to the circuit and used an "old" 3.7v lithium battery (taken from a broken Motorola Defy smartphone) to power it.

A long time ago I bought an IR Kit for Arduino from DFRobot and it came with an useful IR remote control. Using the sample source code and wiring diagram available at the DFRobot's wiki, I managed to identify the frequencies related to all buttons from the remote control.

To be able to use the lithium battery to power Arduino, I took an USB female plug from an old USB hub and, following the USB Pinout description available here, I simply connected the VCC and GROUND pins to the + and - battery pins, respectively, as illustrated at the picture below.

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The IR receiver module specifies 5V for power supply. As I was planning on using 3.7V for powering Arduino, I didn't bother to connect the IR receiver's VCC pin at Arduino's 3V3 pin, and give it less power than I was "required" to. And guess what, it worked like a charm!

New wiring diagram:0

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Necessary library for the IR module: IRremote.zip

Source code