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On the Information Theoretic Performance Comparison of Causal Video coding and Predictive Video coding

IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第3期60卷 1428-1446页

作者： Yang, En-Hui Zheng, Lin He, Da-Ke Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada BlackBerry Waterloo ON N2L 5S8 Canada

Causal video coding is a coding paradigm where video source frames X-1, X-2,..., X-N are encoded in a frame-by- frame manner, the encoder for each frame can use all previous source 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 Xk itself as a source X-k = {X-k(i)}(i = 1)(infinity).Let R-c(*) (D-1,..., D-N) (R-p(*)(D-1,..., D-N), respectively) denote the minimum total rate required to achieve a given distortion level D-1,..., D-N in causal video coding (predictive video coding, respectively). We first show that like R-c(*) (D-1,..., D-N), for jointly stationary and totally ergodic sources X-1, X-2,..., X-N, R-p(*)(D-1,..., D-N) is equal to the infimum of the nth order total rate distortion function Rp, n(D-1,..., D-N) over all n, where R-p(*), n(D-1,..., D-N) itself is given by the minimum of an information quantity over a set of auxiliary random variables. We then prove that if the jointly stationary and totally ergodic sources X-1,..., X-N form a (first-order) Markov chain, we have R-p(*)(D-1,..., D-N) = R-c(*) (D-1,..., D-N). However, this is not true in general if X-1,..., X-N do not form a (first-order) Markov chain. Specifically, we demonstrate that for independent and identically distributed vector source (X-1,..., X-N), if X-1,..., X-N do not form a (first-order) Markov chain, then under some conditions on source frames and distortion, R-c(*) (D-1,..., D-N) is strictly less than R-p(*)(D-1,..., D-N) in general. Our techniques allow us to c

关键词： Causal video coding iterative algorithm more and less coding theorem predictive video coding rate distortion theory stationary ergodic sources

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

Rate Distortion Theory for Causal Video Coding: Characteriza...

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作者： Zheng, Lin University of Waterloo

学位级别：master

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 X?,i=1,2,...,N, are encoded in a frame by frame manner, the encoder and decoder for each frame X?, i =1, 2, ..., N, enlist help only from all previous encoded frames Sj, j=1, 2, ..., *** 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 X? can use all previous original frames Xj, j=1, 2, ..., i-1, and all previousencoded frames Sj, while the corresponding decoder can use only allprevious encoded frames. We consider all studies, comparisons, and designs on causal video codingfrom an information theoreticpoint of view. Let R*c(D?,...,D_N) (R*p(D?,...,D_N), respectively) denote the minimum total rate required to achieve a given distortion level D?,...,D_N > 0 in causal video coding (predictive video coding, respectively). A novel computationapproach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R*c(D?,...,D_N) required to achieve a given distortion (quality) level D?,...,D_N > ***, we first show that for jointly stationary and ergodicsources X?, ..., X_N, R*c(D?,...,D_N) is equalto the infimum of the n-th order total rate distortion functionR_{c,n}(D?,...,D_N) over all n, whereR_{c,n}(D?,...,D_N) itself is given by the minimum of aninformation quantity over a set of auxiliary random variables. Wethen present an iterative algorithm for computingR_{c,n}(D?,...,D_N) and demonstrate the convergence of thealgorithm to the global minimum. The gl

关键词： causal video coding iterative algorithm multi-user information theory predictive video coding rate distortion theory more and less coding theorem

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