GF (q) Precoding: Mutual information analysis in AWGN channels
Bibliographic record
Abstract
In this paper, we propose a new precoding scheme that can introduce correlation between the original transmitted symbols. The precoding process is based on the operations in Galois Field with size q = 2m(GF (q)). In the existing precoding schemes such as orthogonal space-time block code, the generated symbols carry the information of all coded symbols; this correlation can be utilized by the receiver to provide diversity in space and time domain. Similarly, the proposed precoding scheme that utilizes the operations defined in GF (q) can also introduce such correlation. We evaluate the mutual information of the system and conclude that mutual information is always no less than that in the system without the proposed precoding scheme regardless of the source distribution. In addition, when the source is uniformly distributed, the proposed GF (q) precoding scheme achieves the maximum mutual information of the channel, i.e. channel capacity. Hence, we can derive that the proposed precoding scheme in GF (q) can preserve source information during the transmission in the channel. Convinced by the potential benefit of the increased mutual information, the proposed GF (q) precoding scheme is promising in approaching channel capacity.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".