Improved tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN and block fading channels
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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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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 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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