On the information theoretic performance comparison of causal video coding and predictive video coding

Causal video coding is a coding paradigm where video source frames X₁, X₂, ..., X_N 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 the special case where the encoder for each frame X_k is further restricted to enlist help only from all previous encoded frames, causal video coding is reduced to predictive video coding, which all MPEG-series and H-series video coding standards proposed so far are based upon. In this paper, we compare the rate distortion performance of causal video coding with that of predictive video coding from an information theoretic perspective by modeling each frame X_k itself as a source X_k = {X_k(i)}_i=1^∞. Let R_c*(D₁, ..., D_N) (R_p*(D₁, ..., D_N), respectively) denote the minimum total rate required to achieve a given distortion level D₁, ..., D_N >; 0 in causal video coding (predictive video coding, respectively). In the case of TV = 3, we first derive a single-letter characterization of R_p*(D₁, D₂, D₃) for an independent and identically distributed (IID) vector source (X₁, X₂, X₃) where X₁ and X₂ are independent, and then demonstrate that if X₁, X₂, X₃ do not form a (first-order) Markov chain, then under some conditions on source frames and distortion, R_c*(D₁, D₂, D₃) is strictly less than R_p*(D₁, D₂, D₃).