Optimal Precoder and Symbol Grouping for Bandwidth-Efficient Bit-Interleaved Coded Modulation over NAF Single-Relay Channels
Bibliographic record
Abstract
This paper considers the precoder design for a bandwidth-efficient bit-interleaved coded modulation (BICM) over non-orthogonal amplify-and-forward (NAF) single-relay channels with an arbitrary length of cooperative frame 2N. Based on the tight union bound on the bit error probability (BEP), we first derive an asymptotic design criterion with regard to a general 2N × 2N rotation matrix. This expression allows us to develop a class of precoder that not only achieves full cooperative diversity but also optimizes the asymptotic error performance. Interestingly, the developed class of optimal precoder indicates that the source should be kept silent in the cooperative phase. In the broadcasting phase, it is shown that power is distributed equally to 2N information symbols at the source. By further examining the structure of the optimal class of 2N × 2N precoders, we then reveal that precoding over a group of at least 2 information symbols is sufficient to fully exploit diversity and coding advantages. Such precoding technique, which is referred to as symbol grouping, therefore significantly reduces the system complexity without degrading the error performance.
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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 | 0.002 |
| 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 | 0.001 |
| 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 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".