A Systematic Approach to Modified BCJR MAP Algorithms for Convolutional Codes
Bibliographic record
Abstract
Since Berrou, Glavieux and Thitimajshima published their landmark paper in 1993, different modified BCJR MAP algorithms have appeared in the literature. The existence of a relatively large number of similar but different modified BCJR MAP algorithms, derived using the Markov chain properties of convolutional codes, naturally leads to the following questions. What is the relationship among the different modified BCJR MAP algorithms? What are their relative performance, computational complexities, and memory requirements? In this paper, we answer these questions. We derive systematically four major modified BCJR MAP algorithms from the BCJR MAP algorithm using simple mathematical transformations. The connections between the original and the four modified BCJR MAP algorithms are established. A detailed analysis of the different modified BCJR MAP algorithms shows that they have identical computational complexities and memory requirements. Computer simulations demonstrate that the four modified BCJR MAP algorithms all have identical performance to the BCJR MAP algorithm.
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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 | 0.000 | 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".