Rate Distortion Theory for Causal Video Coding: Characterization, Computation Algorithm, Comparison, and Code Design

Due to the sheer volume of data involved, video coding is an important application of lossy source coding, and has received wide industrial interest and support as evidenced by the development and success of a series of video coding standards. All MPEG-series and H-series video coding standards proposed so far are based upon a video coding paradigm called predictive video coding, where video source frames X1, X2, · · · , XN are encoded in a frame by frame manner, the encoder and decoder for each frame Xk, k = 1, 2, · · · , N , enlist help only from all previous encoded frames Sj , j = 1, 2, · · · , k− 1. In this thesis, we will look further beyond all existing and proposed video coding standards, and introduce a new coding paradigm called causal video coding, in which the encoder for each frame Xk can use all previous original frames Xj, j = 1, 2, · · · , k − 1, and all previous encoded frames Sj , while the corresponding decoder can use only all previous encoded frames. We consider all studies, comparisons, and designs on causal video coding from an information theoretic point of view by modeling each frame Xk itself as a source Xk = {Xk(i)}i=1. Let R∗ c(D1, · · · , DN) (R∗ p(D1, · · · , DN), respectively) denote the minimum total rate required to achieve a given distortion level D1, · · · , DN > 0 in causal video coding (predictive video coding, respectively). A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R∗ c(D1, · · · , DN) required to achieve a given distortion (quality) level D1, · · · , DN > 0. Specifically, we first show that for jointly stationary and ergodic sources X1, X2, · · · , XN , R∗ c(D1, · · · , DN) is equal to the infimum of the nth order total rate distortion function Rc,n(D1, · · · , DN) over all n, where Rc,n(D1, · · · , DN) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then present an iterative algorithm for computing Rc,n(D1, · · · , DN) and demonstrate the convergence of the algorithm to the global