Unless you are in an arid area, putting carpet directly over a concrete basement floor, or even over the tile attached to the concrete is inviting mold growth.

The problem isn't usually moisture wicking up from the concrete, but rather summer humidity in the air condensing on the cooler floor, which if there's carpet, results in an environment that fosters mold growth in the carpet.

The best solution is to install a subfloor that provides an air gap (e.g., DriCore, Platon, etc.), and then install the carpet over that.