Further results on the sphere decoder
Bibliographic record
Abstract
The fast development of digital communications hardware allows for the application of very powerful algorithms at the expense of a small increase in complexity compared to the traditionally implemented algorithms. In this paper we give further results on the sphere decoder (SD) algorithm, and its applications to a broad range of digital communications problems related to the separation of m independent sources by n sensors. First, we discuss practical implementation issues and propose an efficient method to initialize the SD parameters based on computing an estimate of the packing radius of the lattice. We relate the initializing method to the expected performance of the SD, and show that at high SNR, one obtains near optimum performance. The complexity of the SD is then shown to be much less than the upper bound on the complexity of the Fincke and Pohst (1985) algorithm for the problem of finding short length vectors in an m-dimensional lattice. Simulations show that the SD of an m-dimensional lattice needs at most O(m/sup 4.5/) arithmetic operations at low SNR, and O(m/sup 3/) at high SNR. The obtained results offer a very powerful tool to reach near the maximum likelihood (ML) decoding performance in several cases such as lattice codes decoding over the Gaussian and Rayleigh fading channels, multiuser detection, uncoded multi-antenna systems detection and space-time codes decoding, and vector quantization.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.004 |
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".