Efficient bit allocation under multiple constraints on cumulated rates for delayed video coding

We consider optimal encoding of a sequence of video units under a given set of rate constraints which may arise from finite codec delay, finite channel capacity, and finite codec buffer sizes. A Lagrange-multiplier approach is employed and some useful properties of the optimal Lagrange- multiplier solution are obtained under the assumption that the allowed video data rates are continuous. Based on these properties, we derive two solution algorithms for discrete allocation. The algorithms are more efficient than that have been presented to date. The solution is optimal when the distortion-rate relations of the video units are convex and the selectable rates of the video units are uniformly spaced with the same granularity. When these conditions do not hold, the Lagrange-multiplier solution may be suboptimal, but can be improved or optimized by a search about the solution.