Ice smells and tastes funny?

Hi. I have a frigidaire refrigerator that has a built in ice and water through the door. Recently my ice has started smelling and tasting funny. Kind of smells like rotting broccoli or some vegitable. I cleaned out both the fridge and freezer and threw out older (but not rotting) veggies and it is still there. I tried replacing the water filter (was time anyway) and it is still there. Any suggestions? Thanks!