Design of multi-edge-type LDPC codes for high-order coded modulation
Bibliographic record
Abstract
A design method for bandwidth-efficient LDPC coded modulation for 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m</sup> -QAM constellations at rate (2m - 1)/(2m) in complex AWGN is presented. A multi-edge-type parameterization is used to exploit the distinct bit-channel capacities unique to high-order modulation using LDPC structures. EXIT analysis is adapted to multi-edge by introducing multi-dimensional EXIT iterated-function system analysis. Under this conceptualization, a successful decoding condition is developed by estimating fixed points of the dynamical system using its numerical gradient. Optimized ensembles are found for 16-QAM with thresholds matching the best known ensembles of equal complexity. For 64 to 1024-QAM, sufficiently high bit-channel capacities allow for extension of lower-order optimized ensembles, leading a practical nested code structure. The nested structure provides flexible rate selection with a single decoder. The gap to constrained, non-iterative capacity of all optimized code ensembles of maximum variable degree of 15 is within 0.21 dB.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".