Improved tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN and block fading channels
Bibliographic record
Abstract
Recently, the added-hyperplane (AHP) bound was proposed on the foundation of the tangential sphere bound (TSB) of Poltyrev. AHP utilises a Bonferroni-type inequality (known as the Hunter bound) together with the Gallager first bounding technique (GFBT) and is tighter than TSB; however, it suffers from a performance-degrading overhead. Another inequality from the Hunter-bound family is applied to the GFBT and a novel technique has been proposed to waive the need for global geometrical properties of the code, removing the aforementioned overhead. Also, a star-structured graph is proposed as the corresponding spanning tree for the Hunter bound. The improved tangential sphere bound (ITSB) is tighter than TSB and AHP and does not impose any overhead or extra optimisation. ITSB is thus the tightest upper bound on the performance of linear binary block codes over AWGN channel. ITSB is then applied to different block (slow) fading channels as well as low-density parity-check codes.
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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 | 0.003 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".