Designing irregular LPDC codes using EXIT charts based on message error rate
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Bibliographic record
Abstract
A new analysis of irregular low density parity check (LDPC) codes on AWGN channels based on modified extrinsic information transfer (EXIT) charts is presented. We modify EXIT charts to track the message error rate transfer characteristics of the constituent codes. Previous analyses, which make a Gaussian assumption for all messages passed, are inaccurate at low SNRs. We more accurately track the message error rate transfer by making a Gaussian approximation only for messages sent from variable nodes, with statistics of messages from check nodes computed by simulation. This makes the analysis more accurate, particularly for low rate codes where, at low SNR, the messages from check nodes are far from Gaussian. The new analysis simplifies understanding of the irregular codes to the level of regular case, leading to a simple approach to the design of irregular codes. We have used this method to design irregular LDPC codes that perform close to the Shannon limit over a wider range of rates and variable degrees as compared to previous work. The same method can be used for many other codes defined on graphs.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 it