Deep Learning-based List Sphere Decoding for Faster-than-Nyquist (FTN) Signaling Detection
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Bibliographic record
Abstract
Faster-than-Nyquist (FTN) signaling is a candidate non-orthonormal transmission technique to improve the spectral efficiency (SE) of future communication systems. However, such improvements of the SE are at the cost of additional computational complexity to remove the intentionally introduced intersymbol interference. In this paper, we investigate the use of deep learning (DL) to reduce the detection complexity of FTN signaling. To eliminate the need of having a noise whitening filter at the receiver, we first present an equivalent FTN signaling model based on using a set of orthonormal basis functions and identify its operation region. Second, we propose a DL-based list sphere decoding (DL-LSD) algorithm that selects and updates the initial radius of the original LSD to guarantee a pre-defined number N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> of lattice points inside the hypersphere. This is achieved by training a neural network to output an approximate initial radius that includes N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> lattice points. At the testing phase, if the hypersphere has more than N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> lattice points, we keep the N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> closest points to the point corresponding to the received FTN signal; however, if the hypersphere has less than N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> points, we increase the approximate initial radius by a value that depends on the standard deviation of the distribution of the output radii from the training phase. Then, the approximate value of the log-likelihood ratio (LLR) is calculated based on the obtained N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> points. Simulation results show that the computational complexity of the proposed DL-LSD is lower than its counterpart of the original LSD by orders of magnitude.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| 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 it