Distribution Matching for Probabilistic Shaping and Stealth Communication: Theory and Algorithms
Bibliographic record
Abstract
Distribution matching refers to the reversible approximation of non-uniform sources using a uniform memoryless source. Applications of distribution matching include probabilistic shaping to facilitate reliable communication at rates closer to capacity, and stealth communication to conceal the presence of information transmission from an eavesdropper. This work considers the design of efficient distribution matching schemes for these two applications, and investigates the fundamental limits of distribution matching for arbitrary, i.e., not necessarily stationary memoryless, sources. For probabilistic shaping of binary symbols, a general architecture built around a binary linear code is proposed.The linear code operates as a lossy source code, and its rate-distortion performance directly determines the shaping performance of the architecture. Consequently, a strong connection between probabilistic shaping and lossy source coding is revealed. Namely, it is shown that using a rate-distortion optimal linear code to implement the architecture, translates to asymptotically optimal shaping performance. Polar codes, provably optimal for lossy compression, are then used to implement the shaping architecture. Leveraging the special structure of polar codes, and the sufficiently fast rate with which they approach the rate-distortion bound, it is established that the polar coded scheme is optimal for probabilistic shaping and stealth communication, with a linearithmic complexity. For probabilistic shaping of non-binary symbols, a highly customizable parallelized shaping architecture is presented.The architecture operates by combining outputs generated in parallel by several binary-output shaping schemes. A design process subject to constraints on the available resources is explored, highlighting the possibility of realizing different instances of the architecture that achieve various trade-offs between performance, latency and memory requirements. The potential benefits of the proposed scheme are demonstrated via numerical results, comparing the performance-latency-memory trade-offs achievable by different instances of the architecture, against those achievable by other notable schemes. The theoretical portion of this work focuses on the investigation of distribution matching for general sources. The definition of general sources allows for countably infinite source alphabets, and includes a wide range of source classes, such as non-stationary or non-ergodic sources. For such general sources, the optimal distribution matching rate required for stealth communication is derived using information-spectrum methods.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".