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With rapid advances in multimedia and wireless network technologies, it is now feasible to provide live video streaming over wireless networks. However, since bandwidth is a scarce resource in wireless networks, it is important to design an adaptive bandwidth allocation scheme for video streams to make efficient use of wireless bandwidth. In this paper, we propose an adaptive bandwidth allocation scheme for layered video streams using a novel quality assessment metric. Our analysis and simulation results show that the proposed scheme can provide better quality adaptation for video streams when the bandwidth of the underlying wireless channels changes.