A low-complexity generalized sphere decoding approach for underdetermined linear communication systems: performance and complexity evaluation
Bibliographic record
Abstract
For underdetermined linear systems, original sphere decoding (SD) algorithms fail due to zero diagonal elements in the upper-triangular matrix of the QR or Cholesky factorization of the underdetermined matrix. To solve this problem, this paper presents a low-complexity generalized sphere decoding (GSD) approach by transforming the original underdetermined problem into the full-column-rank one so that standard SD can be directly applied on the transformed problem. Since the introduced transformation maintains the dimension of the original problem for all M-QAM's, the proposed GSD approach provides significant reduction in complexity as compared to other GSD schemes, especially for M-QAM with large signaling constellation. Both performance and expected complexity are analyzed to provide the comprehensive relationships between the performance and complexity of the proposed GSD and its parameters. Illustrative simulation and analytical results are in good agreement in terms of both the performance and complexity and indicate that with the properly selected design parameters, the proposed GSD scheme can approach the optimum maximumlikelihood decoding (MLD) performance with low complexity for underdetermined linear communication systems including underdetermined MIMO systems, and the proposed expected complexity analysis can be used as reliable complexity estimation for practical implementation of the proposed algorithm and serve as reference for other GSD algorithms.
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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 | 0.002 | 0.006 |
| 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 | 0.001 |
| 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 | 0.001 |
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".