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We study state-based video communication where a client simultaneously informs the server about the presence status of various packets in its buffer. In sender-driven transmission, the client periodically sends to the server a single acknowledgement packet that provides information about all packets that have arrived at the client by the time the acknowledgment is sent. In receiver-driven streaming, the client periodically sends to the server a single request packet that comprises a transmission schedule for sending missing data to the client over a horizon of time. We develop a comprehensive optimization framework that enables computing packet transmission decisions that maximize the end-to-end video quality for the given bandwidth resources, in both prospective scenarios. The core step of the optimization comprises computing the probability that a single packet will be communicated in error as a function of the expected transmission redundancy (or cost) used to communicate the packet. Through comprehensive simulation experiments, we carefully examine the performance advances that our framework enables relative to state-of-the-art scheduling systems that employ regular acknowledgement or request packets. Consistent gains in video quality of up to 2B are demonstrated across a variety of content types. We show that there is a direct analogy between the error-cost efficiency of streaming a single packet and the overall rate-distortion performance of streaming the whole content. In the case of sender-driven transmission, we develop an effective modeling approach that accurately characterizes the end-to-end performance as a function of the packet loss rate on the backward channel and the source encoding characteristics.