A network linear block coding approach to selective detect-and-forward multi-way relaying
Bibliographic record
Abstract
In this work, we introduce a network linear block coding framework for multi-way relaying with differential MPSK modulation. We consider a system with K user terminals and L relays employing a selective detect-and-forward (DF) relaying protocol. Each relay is associated with a relevant group of terminals. During the first K phases, each terminal broadcasts its own signal to relay nodes and all the other terminals. During the following L phases, each relay forwards a linearly combined signal to all the terminals only if all the symbols from its relevant group were detected successfully. Such a system can be represented as a linear block code in systematic form, where the transmissions over direct links provide the information symbols and the relays form the parity check symbols. Therefore, the decoding at each terminal consists of decoding a (K+L,K) linear block code. We first analyse the theoretical performance of our system with optimal decoding, including pairwise error probability, codeword error probability and bit error rate. It is shown that our system can achieve a diversity order equals to the minimum Hamming distance of the equivalent code when using maximum likelihood decoding. For practical implementation, a sub-optimal decoder based on the log-domain belief propagation algorithm is employed at the terminals. We first present numerical results for short binary and 4-ary codes, and then extend the system to large networks using LDPC codes. Both the theoretical and simulation results demonstrate a significant performance gain of our system over an uncoded scheme. The properties of suitable codes for the proposed system are studied, indicating that high-rate systematic LDPC codes with moderate minimum distance and without small girths are suitable for our system. Furthermore, we derive and apply a hard threshold at the terminals to reduce the performance loss of when the terminals don't know which relay transmits compared to when the terminals know which relay transmits. It is shown that such a hard threshold can improve the performance of our system without adding too much complexity. Finally, realistic relays by thresholding received samples and decision variables are considered. This thesis shows that even with such realistic relays, our system can still outperform the uncoded scheme, at least for the error rates of interest.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.005 |
| 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 teacher head, 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".