Feedback Capacity of a Class of Symmetric Finite-State Markov Channels
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Bibliographic record
Abstract
We consider the feedback capacity of a class of symmetric finite-state Markov channels. Here, symmetry (termed “quasi-symmetry”) is defined as a generalized version of the symmetry defined for discrete memoryless channels. The symmetry yields the existence of a hidden Markov noise process that depends on the channel's state process and facilitates the channel description as a function of input and noise, where the function satisfies a desirable invertibility property. We show that feedback does not increase capacity for such class of finite-state channels and that both their nonfeedback and feedback capacities are achieved by an independent and uniformly distributed (i.u.d.) input. As a result, the channel capacity is explicitly given as a difference of output and noise entropy rates, where the output is driven by the i.u.d. input.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it