Polar Coded Distribution Matching for Probabilistic Shaping and Stealth Communication
Bibliographic record
Abstract
We present a polar coded one-to-many distribution matching scheme. The scheme uses a randomized encoding approach to approximate, in an invertible manner, binary discrete memoryless sources (B-DMSs) using a binary symmetric source. This is accomplished by using polar codes as lossy source codes, and by leveraging their linear structure. Due to the special recursive structure of polar codes, the encoding and decoding complexity of the scheme is of order $\mathcal{O}(N \log N)$, where N denotes the output blocklength. Leveraging the rate-distortion optimality of polar codes, the scheme is shown to be asymptotically optimal for probabilistic shaping and stealth communication over binary output alphabets. Namely, in the limit of large blocklength N, the polar coded scheme is shown to approximate any B-DMS with vanishing Kullback–Leibler divergence and with rate approaching the entropy of the B-DMS.
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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 | 0.001 | 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 | 0.000 |
| 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".