The capacity-cost function of discrete additive noise channels with and without feedback
Bibliographic record
Abstract
We consider modulo-q additive noise channels, where the noise process is a stationary irreducible and aperiodic Markov chain of order k. We begin by investigating the capacity-cost function (C(/spl beta/)) of such additive-noise channels without feedback. We establish a tight upper bound to (C(/spl beta/)) which holds for general (not necessarily Markovian) stationary q-ary noise processes. This bound constitutes the counterpart of the Wyner-Ziv lower bound to the rate-distortion function of stationary sources with memory. We also provide two simple lower bounds to C(/spl beta/) which along with the upper bound can be easily calculated using the Blahut algorithm for the computation of channel capacity. Numerical results indicate that these bounds form a tight envelope on C(/spl beta/). We next examine the effect of output feedback on the capacity-cost function of these channels and establish a lower bound to the capacity-cost function with feedback (C/sub FB/(/spl beta/)). We show (both analytically and numerically) that for a particular feedback encoding strategy and a class of Markov noise sources, the lower bound to C/sub FB/(/spl beta/) is strictly greater than C(/spl beta/). This demonstrates that feedback can increase the capacity-cost function of discrete channels with memory.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".