İphone 5 battery dies in a couple of hours when the cellular data is on

I have been using iPhone 5 for more than a month. I did not have any problems with the battery and wifi connection. 5 days ago my battery began to die in a couple of hours. I leave it %100 full battery at night, when I wake up in the morning it was already shut down. When I closed the cellular data the battery performs as former peformance. Even this battery shortage do not happen when the iphone is connected to wifi. When I open the celullar data even it is connected to a wifi, the battery dies again. I updated to ios 6.0.2 three weeks ago and nothing happened negatively after this update. The battery shortage began suddenly.