Do you know that the Airtel remote is actually working?
It's possible that the Airtel is using a proprietary protocol that the IrRemote library doesn't recognze. I've never used this library, but does it return an error status?
If you have a scope, you can rig up an IR receiver, or an IR phototransistor, or possibly even just a red LED, and capture the remote's output on the scope. But the easiest way is probably extensive Googling to find where someone else has already figured it out.
I have been at the microcontroller hobby for a long time. I used to have a 4 channel digital scope, but it died. I don't have much money so I bought one of those logic analyzers and have not really missed the scope. In the Pulseview software there are a bunch of handy decoders like I2C, SPI, UART that help to interpret a channel's data.