Advances in wireless access technologies such as WiMax and LTE have accelerated the development of wireless video applications. Though existing erasure codes are designed for wireless data broadcasting, their potential can only be realized for wireless video broadcasting if the distortions associated with video packets and their complex decoding dependency are taken into consideration. In this paper, we propose the greedy video erasure code (GVEC) to minimize average video distortion by accounting for the temporal scalable decoding dependency among video frames e.g. I, P and B frames in MPEG. GVEC is a greedy algorithm and suffers from high computational complexity. For practical implementation, we have designed the joint video adaptation and erasure code (JVEC) with lower complexity, which can generate erasure codes on the fly to guarantee the decoding of important video frames. Simulation results show that the performance of JVEC is very close to that of GVEC, and is superior to that of existing erasure codes. Our results also show the existence of a performance tradeoff between video distortion and video packet throughput.