On computing Verdu's upper bound for a class of maximum-likelihood multiuser detection and sequence detection problems
Bibliographic record
Abstract
The upper bound derived by Verdu (1986) is often used to evaluate the bit error performance of both the maximum-likelihood (ML) sequence detector for single-user systems and the ML multiuser detector for code-division multiple-access (CDMA) systems. This upper bound, which is based on the concept of indecomposable error vectors (IEVs), can be expensive to compute because in general the IEVs may only be obtained using an exhaustive search. We consider the identification of IEVs for a particular class of ML detection problems commonly encountered in communications. By exploiting the properties of the IEVs for this case, we develop an IEV generation algorithm which has a complexity substantially lower than that of the exhaustive search. We also show that for specific communication systems, such as duobinary signaling, the expressions of Verdu's upper bound can be considerably simplified.
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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 | 0.020 | 0.106 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.003 | 0.006 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".