Bibliographic record
Abstract
In this dissertation, we study linear programming (LP) decoding of low-density parity-check (LDPC) codes based on the alternating direction method of multipliers (ADMM) technique, or ADMM decoding for short.The decoding of LDPC codes is formulated as an LP model and solved efficiently by the ADMM technique.However, compared with traditional belief-propagation decoding, ADMM decoding suffers from higher complexity and worse error correction performance, which prevents the employment of ADMM decoding in reality.To reduce the complexity of ADMM decoding, we first focus on the simplification of the check polytope projection, the most complex operation in ADMM decoding.We propose an iterative check polytope projection algorithm without the sorting operation.The proposed algorithm converges with the increase of iterations.Moreover, for a fixed number of iterations, its average complexity and the worst-case complexity are linear in the input dimension.Another direction we propose to simplify ADMM decoding is to devise a better scheduling scheme than the standard flooding scheme.We start from the node-wise scheduling scheme which only updates the check node messages with the maximum message residual.Then we simplify the calculation of the message residual and propose a reduced-complexity node-wise scheduling scheme.To improve the error correction performance of ADMM decoding, we propose a novel ADMM penalized decoding algorithm whose penalty term is based on check nodes (CN).We investigate the properties of the CN penalty functions and show several examples.We make conclusions on its convergence properties and prove its failure probability is independent of the transmitted codewords for symmetric channels.Monte-Carlo simulation and the instanton analysis show its better error correction performance in the low and high SNR regions.Finally, we propose a post-processing technique to lower the error floor of LDPC codes.The output of the first stage decoder can be revised if the syndrome is found This is a journey with joys and tears.I encountered many amazing people.They instructed me, helped me, and accompanied me.First of all, I would like to thank Prof. Amir H. Banihashemi for his guidance.His attitudes towards the research and devotion to one specific area are impressive.All these will have a life-long influence on me.It is also a great time working with people in his coding research group.I have a great memory of learning from their presentations.Next, I should thank Prof.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
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".