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

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.