Analysis of Low-Density Parity-Check Codes for the Gilbert–Elliott Channel
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Bibliographic record
Abstract
Density evolution analysis of low-density parity-check (LDPC) codes in memoryless channels is extended to the Gilbert-Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum-product algorithm (SPA) is used to perform LDPC decoding jointly with channel-state detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space point-by-point. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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 it