Bandwidth-Efficient Bit-Interleaved Coded Modulation Over NAF Relay Channels: Error Performance and Precoder Design
Bibliographic record
Abstract
This paper investigates the error performance and precoder design for a bandwidth-efficient bit-interleaved coded modulation (BICM) system over a nonorthogonal amplify-and-forward (NAF) half-duplex single-relay channel. A tight union bound on the asymptotic bit error probability (BEP) is first derived for an arbitrary block length of 2N, which corresponds to the case of using a 2N× 2Nprecoder. This bound provides a useful tool for predicting the error performance. Attention is then paid to the coded NAF system that uses a 2 × 2 precoder, where a closed-form expression of the bound is obtained. Based on this expression, an optimal class of 2 × 2 precoders with respect to the asymptotic performance is then developed. Unlike the optimal precoders that are designed for uncoded systems, the derived precoder indicates that the source only needs to send the superposition of the first symbol and the rotated version of the second symbol in the first time slot while being silent in the remaining slot to achieve the best asymptotic performance. For good convergence property, it is further shown that a rotation angle that maximizes the minimum Euclidean distance of the superposition constellation should be used. An optimal rotation angle is then analytically determined for various modulation schemes. Both analytical and simulation results show that the proposed precoders not only exploit full cooperative diversity but offer a significant coding gain over the optimal precoders for uncoded NAF systems as well.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".