Jar decoding: LDPC coding theorems for binary input memoryless channels
Bibliographic record
Abstract
Recently, a new decoding rule called jar decoding was proposed, under which the decoder first forms a set of suitable size, called a jar, consisting of sequences from the channel input alphabet considered to be closely related to y <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , and then takes any codeword from the jar as the estimate of the transmitted codeword. In this paper, we show that under jar decoding, the analysis of low density parity check (LDPC) codes is much easier compared to maximum a posteriori (MAP) or maximum likelihood (ML) and Belief Propagation (BP) decoding, and new general LDPC coding theorems can be established. Specifically, it is proved that LDPC codes can approach the mutual information, with diminishing bit error probability, of any binary input memoryless channel with uniform input distribution when the average variable node degree is large. Moreover, simulation shows an interesting connection between jar decoding and BP decoding, i.e., BP decoding can be regarded as one of many ways to pick up a codeword from the jar for LDPC codes when it succeeds in outputting a codeword.
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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 | 0.001 | 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 | 0.001 |
| 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".