CTH14-5: Probability Density Functions of Logarithmic Likelihood Ratios in Phase Shift Keying BICM
Bibliographic record
Abstract
Bit-interleaved coded modulation (BICM) is a coded-modulation scheme where the output of the channel encoder and the input of the modulator are separated by a bit- level interleaver. From the decoder's point of view, the modulator, the transmission channel, and the demodulator (calculating bits' reliability metrics) become a memoryless BICM channel with binary inputs and real outputs. The BICM channel's outputs (reliability metrics) are known to be Gaussian for binary-or quaternary phase shift keying but no expression for their probability density function (PDF) is known for higher-order modulation. We fill this gap presenting closed-form expressions for PDF of reliability metrics in BICM based on M-PSK with gray mapping. Such probabilistic description of BICM channel is necessary to calculate the channel's information-theoretic parameters such as capacity, or cut-off rate but it is also a tool required to analyze the performance of coded transmission.
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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 | 0.004 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".