Gamma rate theory for causal rate control in source coding and video coding

• Gamma rate theory for rate control.
• Gamma rate function and rate gamma function.
• New performance metric for evaluating video coding algorithms.

The rate distortion function in information theory provides performance bounds for lossy source coding. However, it is not clear how to causally encode a Gaussian sequence under rate constraints while achieving R–D optimality. This problem has significant implications in the design of rate control for video communication. To address this problem, we take distortion fluctuation into account and develop a new theory, called gamma rate theory, to quantify the trade-off between rate and distortion fluctuation. The gamma rate theory implies that, to evaluate the performance of causal rate controls in source coding, the traditional R–D metric needs to be replaced by a new GRD metric. The gamma rate theory identifies the trade-off between quality fluctuation and bandwidth, which is not known previously. To validate the gamma rate theory, we design a rate control algorithm for video coding; our experimental results demonstrate the utility of the gamma rate theory in video coding.