This paper considers the mean square stabilization problem of discrete-time linear time-invariant systems over a power constrained fading channel. Fundamental limitations on the mean square stabilizability are obtained via information theoretic arguments. For scalar systems and two-dimensional systems, necessary and sufficient conditions for the mean square stabilizability are provided. Moreover, an adaptive time division multiple access (TDMA) communication scheme is designed for high-dimensional systems, which achieves a larger stabilizability region than the conventional TDMA communication scheme, and is proved to be optimal under certain situations.