Time-Division is Optimal for Covert Communication over Some Broadcast\n Channels
Bibliographic record
Abstract
We consider a covert communication scenario where a transmitter wishes to\ncommunicate simultaneously to two legitimate receivers while ensuring that the\ncommunication is not detected by an adversary, the warden. The legitimate\nreceivers and the adversary observe the transmission from the transmitter via a\nthree-user discrete or Gaussian memoryless broadcast channel. We focus on the\ncase where the "no-input" symbol is not redundant, i.e., the output\ndistribution at the warden induced by the no-input symbol is not a mixture of\nthe output distributions induced by other input symbols, so that the covert\ncommunication is governed by the square root law, i.e., at most\n$\\Theta(\\sqrt{n})$ bits can be transmitted over $n$ channel uses. We show that\nfor such a setting, a simple time-division strategy achieves the optimal\nthroughputs for a non-trivial class of broadcast channels; this is not true for\ncommunicating over broadcast channels without the covert communication\nconstraint. Our result implies that a code that uses two separate optimal\npoint-to-point codes each designed for the constituent channels and each used\nfor a fraction of the time is optimal in the sense that it achieves the best\nconstants of the $\\sqrt{n}$-scaling for the throughputs. Our proof strategy\ncombines several elements in the network information theory literature,\nincluding concave envelope representations of the capacity regions of broadcast\nchannels and El Gamal's outer bound for more capable broadcast channels.\n
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 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".