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Layered multicast has been shown as a promising technique for dis-tributing a video program to a potentially large number of heterogeneous re-ceivers. While several layered multicast approaches have been proposed, prior work has almost exclusively focused on improving the perceived video quality in terms of PSNR value or/and the fairness among different receivers. In this paper, we first argue that stability is another major index for the video playback quality; in an extreme case even with the best possible achievable PSNR value, the frequent switching between different layers still can lead to significant qual-ity degradation. We then introduce an end-to-end adaptation framework that improves the stability and fairness for receivers by employing a dynamic layer rate allocation scheme on the sender's side. Specifically, we propose a new metric, called Stability-aware Fairness Index (SFI), which can capture both the stability as well as fairness. We then formulate the optimal layer rate allocation problem with the objective of minimizing the expected SFI for all the receivers in a multicast session, and derive an efficient algorithm to solve the problem. Simulation results demonstrate that our scheme can significantly improve the degree of stability and fairness, thus leading to better video playback quality. [ABSTRACT FROM AUTHOR]