The transmitter code has been provided in the files section. 

Connect pin 0.9 (UART 1 - RX) to the data pin. Also make the appropriate Vdd and ground connections. The received signal is then repeatedly transmitted through 0.0 (UART0 - RX) to the data pin of FS1000A Transmitter. This is done so that the receiver does not pick up noise in between successive transmissions.   The schematic of the transmitter side and our circuit can be seen as follows:

At the receiver end, we have 0.9 (UART1 -RX) connected to the data pin of FS1000A Receiver. This is then decoded (code is attached in one of the previous sections) using a look-up table. Support for more keys can be added. The LCD is also initialized to assist in debugging.  The schematic and the circuit can be seen below:

The receiver LPC is flashed with the receiver code, with the ISP jumper in place. After flashing, the ISP jumper is removed, and placed to connect the JTAG pins. Any value pressed in the PS/2 keyboard should ideally appear on the LCD screen. If it does not, then wait for some time for the receiver to perform gain adjustment. Now the received values must automatically write into any open text editor window.