Gallager first bounding technique for the performance evaluation of maximum-likelihood decoded linear binary block codes
Bibliographic record
Abstract
Exact bit or frame error rate expressions for most communication systems are either too complex or unlikely to exist in nice closed forms. A good alternative is to bound the performance measure by tight enough lower and upper bounds. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). In this method, Gallager splits the error probability to the joint probability of error and noise residing in a region $\Re$ (here referred to as the Gallager region) plus joint probability of error and noise residing in the complement of $\Re$ (also referred to as regions of many and few errors, respectively); where $\Re$ is a volume around the transmitted codeword. A comprehensive study of a number of upper bounds on the error probability of ML decoding of binary codes based on GFBT is provided. For some bounds, their applicability to other schemes and channels is also pointed out and argued.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.048 |
| Meta-epidemiology (narrow) | 0.004 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".