Waterfall Performance Analysis of Finite-Length LDPC Codes on Symmetric Channels
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Bibliographic record
Abstract
An efficient method for analyzing the performance of finite-length low-density parity-check (LDPC) codes in the waterfall region, when transmission takes place on a memoryless binary-input output-symmetric channel is proposed. This method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite-length codeword. We model these variations with a single parameter. This parameter is then viewed as a random variable and its probability distribution function is obtained. Assuming that a decoding failure is the result of an observed channel worse than the codeiquests decoding threshold, the block error probability of finite-length LDPC codes under different decoding algorithms is estimated. Using an extrinsic information transfer chart analysis, the bit error probability is obtained from the block error probability. Different parameters can be used for modeling the channel variations. In this work, two of such parameters are studied. Through examples, it is shown that this method can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 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