Gaussian wiretap channel with shared keys between transmitter and helpers
Bibliographic record
Abstract
We study the secure degrees of freedom (d.o.f.) of helper-assisted Gaussian wiretap channel with shared key between the transmitter and the helper. Given that the rate of the key scales with power as γ/2 log SNR, we show that secure d.o.f. is min{1+γ / 2, 1}. The achievability proof combines real interference alignment with the artificial noise transmission technique. Using the shared key we sample common artificial noise symbols from a PAM constellation at the transmitter and the helper and transmit them in the null space of the legitimate receiver's channel. We further sample independent noise symbols, also from the same PAM constellation, at the transmitter and the helper and align these symbols at the legitimate receiver. The noise symbols together occupy sufficient dimensions to mask the message at the eavesdropper. A converse proof, which extends the technique of Xie and Ulukus to incorporate common randomness, establishes the optimality of secure d.o.f..We also extend the result to the case with M helpers with two different assumptions on the key sharing structure: the transmitter shares a common key or distinct keys with the M helpers. The exact secure d.o.f.s for these two cases, before they saturate to 1, are proved to be M+γ /M+1 and M+Mγ/M+1 respectively.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".