A closed-form symbol error rate analysis for successive interference cancellation decoders
Bibliographic record
Abstract
Wireless and digital communications applications require the detection of an integer vector x̂ from y = Ax̂ + v, where A ϵ ℝm×nis a random matrix whose entries are independent and identically distributed (i.i.d.) standard Gaussian N(0,1) entries, and v ϵ ℝmis a noise vector following the Gaussian distribution N(0,σ2) with given σ. The successive interference cancellation (SIC) decoders are frequently used to detect x̂ due to their high accuracy and low implementation complexity. However, to accurately characterize their performance, we need to analyze their symbol error rates (SER). In this paper, we derive a closed-form expression for the SER of the SIC decoders and investigate its properties. Simulated error probabilities of the SIC decoders agree closely with our theoretical expressions.
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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 | 0.007 | 0.022 |
| Meta-epidemiology (narrow) | 0.004 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| 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".