Precoding for the AWGN Channel With Discrete Interference
Bibliographic record
Abstract
For a state-dependent discrete memoryless channel with input alphabet${\cal X}$, state alphabet${\cal S}$, and output alphabet${\cal Y}$where the independent and identically distributed (i.i.d.) state sequence is known causally at the transmitter, it is shown that by using at most$\min \{\vert{\cal X}\vert \vert{\cal S}\vert -\vert{\cal S}\vert +1,\vert{\cal Y}\vert \}$out of$\vert{\cal X}\vert^{\vert{\cal S}\vert}$inputs of the Shannon's derived channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter,$M$-ary signal transmission for the additive white Gaussian noise (AWGN) channel with additive$Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. The optimal precoding scheme is derived under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet. It is shown that at low signal-to-noise ratio (SNR) not doing precoding is optimal. For the special case where the Gaussian noise power is zero, it is shown that the rate$\log_2 M$is achievable by a one-shot coding scheme if${\cal X}$is an arithmetic progression.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".