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

• Published in: IEEE transactions on information theory Vol. 57; no. 8; pp. 5258 - 5280
• Main Authors: Yang, En-Hui, Zheng, Lin, He, Da-Ke, Zhang, Zhen
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Byproducts; Causal video coding; Codes; Coding; Coding, codes; Computation; Convergence; Correlation analysis; Decoding; Distortion; Encoding; Exact sciences and technology; extended Markov lemma; Frames; Image processing; Information theory; Information, signal and communications theory; iterative algorithm; Markov processes; Mathematical models; multi-user information theory; predictive video coding; Random variables; rate distortion characterization and computation; rate distortion theory; Rate-distortion; Signal and communications theory; Signal processing; stationary ergodic sources; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Video coding; Video coding; Multiple access; predictive video coding; rate distortion characterization and computation; stationary ergodic sources; extended Markov lemma; Video signal; Rate distortion theory; Causal video coding; Ergodicity; Iterative method; Decoding; Algorithm; iterative algorithm; Video signal processing; Algorithm performance; Predictive coding; Convergence rate; Causality; Information theory; multi-user information theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2159043

Causal video coding is considered from an information theoretic point of view, where video source frames X 1 , X 2 , ..., X N are encoded in a frame by frame manner, the encoder for each frame X k can use all previous frames and all previous encoded frames while the corresponding decoder can use only all previous encoded frames, and each frame X k itself is modeled as a source X k = {X k (i) } i=1 ∞ . A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding R c *(D 1 , ...,D N ) required to achieve a given distortion (quality) level D 1 , ...,D N >; 0. Among many other things, the computation approach includes an iterative algorithm with global convergence for computing R c *(D 1 , ...,D N ) . The global convergence of the algorithm further enables us to demonstrate a somewhat surprising result (dubbed the more and less coding theorem)-under some conditions on source frames and distortion, the more frames need to be encoded and transmitted, the less amount of data after encoding has to be actually sent. With the help of the algorithm, it is also shown by example that R c *(D 1 , ...,D N ) is in general much smaller than the total rate offered by the traditional greedy coding method. As a by-product, an extended Markov lemma is established for correlated ergodic sources.