Real-Time Communication Systems based on Taut Strings

We consider buffered real-time communication over channels with time-dependent capacities which are known in advance. The real-time constraint is imposed in terms of limited transmission time between sender and receiver. For a network consisting of a single channel it is shown that there is a coding rate strategy, geometrically characterized as a taut string, which minimizes the average distortion with respect to all convex distortionrate functions. Utilizing the taut string characterization further, an algorithm that computes the optimal coding rate strategy is provided. We then consider more general networks with several connected channels in parallel or series with intermediate buffers. It is shown that also for these networks there is a coding rate strategy, geometrically characterized as a taut string, which minimizes the average distortion with respect to all convex distortion-rate functions. The optimal offline strategy provides a benchmark for the evaluation of different coding rate strategies. Further, it guides us in the construction of a simple but rather efficient strategy for channels in the online setting which alternates between a good and a bad state.