An upper bound on BER in a coded two-transmission scheme with same-size arbitrary 2D constellations
Bibliographic record
Abstract
Constellation design is a well studied topic. For instance, it is known that, when 2-dimensional (2D) signalling schemes are used, the performance gains that the optimal constellations yield in comparison to the commonly employed square constellations are rather small. However, most of the earlier literature in this area considers rather simple communication protocols (for instance, without retransmissions), even in the absence of channel coding. With the advent of advanced communication protocols as well as signal processing techniques, there has been a rejuvenated interest in constellation design in recent years. In this paper, we consider a generic two-transmission scheme which may correspond to a relay, HARQ (hybrid automatic repeat request), or CoMP (coordinated multipoint) based transmission scenario, with a maximum likelihood receiver. The system has the flexibility of using a different 2D constellation in each transmission (however, the constellation size, i.e., the number of bits per symbol, remains the same). A generic channel coding scheme for which an encoder transfer function can be written (such as, convolutional and turbo codes) is considered for the versatile Nakagami-m fading channel. The main contribution of this paper is the derivation of an upper bound on the bit error rate (BER) which is expressed as a function of the distances between the constellation points. Using proper optimization techniques, this bound (tight for the high SNR values) which captures the impact of the distances between the constellation points can enable the design of good constellations for a given coding scheme in the above explained two-transmission setting.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".