Optimal bit allocation in the presence of quantizer feedback

The authors consider the problem of optimal bit allocation in various forms of predictive coding, where the predictor itself has errors resulting from previous quantization. The solution to this problem has potential application to many forms of image and video coding where predictive coding is used. In predictive coding, the input to the quantizer can be decomposed into the innovation, i.e., the part of the quantizer input signal due to the quantization of the predictor. The natural question that arises is whether it is better to allocate more bits to the predictor, since quantization errors persist longer, or to allocate more bits to coding the total residual. This problem is analyzed for predictive video coding through the use of a simple parametric distortion-rate model for the propagation of quantization errors. This model provides a framework in which the optimal bit allocation problem can be solved in the presence of quantizer feedback. An exact MMSE (minimum mean-square error) solution is obtained that involves solving one nonlinear monotonic equation for one Lagrange multiplier, after which the bit allocation has a closed-form analytic solution. Since the MMSE solution does not produce equal distortion in all frames, the optimal MINMAX (minimize the maximum) bit allocation that minimizes the frame distortion subject to equal distortions per frame is also introduced.<>