Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes
Bibliographic record
Abstract
The optimal zero delay coding of a finite-state Markov source is considered. The existence and structure of optimal codes are studied using a stochastic control formulation. Prior results in the literature established the optimality of deterministic Markov (Walrand–Varaiya-type) coding policies for the finite time horizon problem, and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem. Our main result here shows that for any irreducible and aperiodic Markov source with a finite alphabet,deterministic and stationaryMarkov coding policies are optimal for the infinite horizon problem. In addition, the finite block length (time horizon) performance of an optimal (stationary and Markov) coding policy is shown to approach the infinite time horizon optimum at a rate$O(1/T)$. The results are extended to systems, where zero delay communication takes place across a noisy channel with noiseless feedback.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".