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In this correspondence, we propose a constant quality rate allocation algorithm for fine granularity scalability (FGS) coded videos. The rate allocation problem is formulated as a constrained minimization of quality fluctuation. The minimization is solved using a composite rate distortion (R-D) analysis. For a set of video frames, a composite R-D curve is first computed and then used for computing the optimal rate allocation. This algorithm is efficient because it is neither iterative nor recursive. After the composite R-D curve is computed, it can be used for optimal rate allocation of any rate budget. Moreover, the composite R-D curve can be updated efficiently over sliding windows. Experimental results have shown both the effectiveness and the efficiency of the proposed algorithm.