On optimum fixed-rate causal scalar quantization design for causal video coding

Causal video coding is a coding paradigm where video source frames are encoded in a frame by frame manner, the encoder for each frame can use all previous frames and all previous encoded frames, and the corresponding decoder can use only all previous encoded frames. In this paper, the design of causal video coding is considered from an information theoretic perspective by modeling each frame as a stationary information source. We first put forth a concept called causal scalar quantization. By extending the classic Lloyd-Max algorithm for a single source to this multiple sources case, we then propose an algorithm for designing optimum fixed-rate causal scalar quantizers for causal video coding to minimize the total distortion among all sources. The proposed algorithm converges in the sense that the total distortion cost is monotonically decreasing until a stationary point is reached. Simulation results show that in comparison with fixed-rate predictive scalar quantization, fixed-rate causal scalar quantization offers as large as 16% quality improvement (distortion reduction).