On the rate distortion theory for causal video coding
Bibliographic record
Abstract
Causal video coding is considered from an information theoretic point of view, where video source frames X1, X2, ..., XNare encoded in a frame by frame manner, the encoder for each frame Xk, k = 1, ..., N, can use all previous frames and all previous encoded frames while the corresponding decoder can use only all previous encoded frames, and each frame Xkitself is modeled as a source Xk= {Xk(i)}i=1infin. A novel computation approach is proposed to analytically characterize, numerically compute, and compare the minimum total rate of causal video coding Rc(D1, ..., DN) required to achieve a given distortion (quality) level D1, ..., DNges 0. Specifically, we first show that for jointly stationary ergodic sources X1, X2, ..., XN, Rc(D1, ..., DN) is equal to the infimum of the nth order total rate distortion function Rc,n(D1, ..., DN) over all n, whereRc,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 minimum. The global convergence of the algorithm further enables us to establish a single-letter characterization of Rc(D1, ...,DN) in a novel way when the N sources are an independent and identically distributed (IID) vector source. With the help of the algorithm, we also demonstrate a 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 has to be actually sent. Predictive video coding, where each encoder and its corresponding decoder can use only all previous encoded frames, is also investigated.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".