Error Performance Analysis of BPSK Modulation in Physical-Layer Network-Coded Bidirectional Relay Networks
Bibliographic record
Abstract
We analyze the error performance of the physical-layer network coding (PNC) protocol without channel coding in bidirectional relay networks for binary phase shift keying (BPSK) over Rayleigh fading channels. It is assumed that a bidirectional relay network consists of two sources and a relay, where each node has a single antenna and operates in a half-duplex mode, and the PNC over finite GF(2) is employed. In this system, since the maximum-likelihood (ML) detection metric of the multiple access channel (MAC) at the relay is given by the sum of two exponential functions, it is not possible to utilize the classical Euclidean distance rule. To make the performance analysis tractable, we approximate the ML detection metric by adopting the max-log approximation. Then we derive tight upper and lower bounds in closed form for the average symbol error probability of the MAC at the relay. Finally, we obtain tight upper and lower bounds in closed form for the end-to-end average bit-error rate (BER).
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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 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".