Precoding for the AWGN Channel With Discrete Interference
Bibliographic record
Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> For a state-dependent discrete memoryless channel with input alphabet <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">${\cal X}$</tex></formula></emphasis>, state alphabet <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">${\cal S}$</tex></formula></emphasis>, and output alphabet <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">${\cal Y}$</tex></formula></emphasis> 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 <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\min \{\vert{\cal X}\vert \vert{\cal S}\vert -\vert{\cal S}\vert +1,\vert{\cal Y}\vert \}$</tex></formula></emphasis> out of <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\vert{\cal X}\vert^{\vert{\cal S}\vert}$</tex></formula></emphasis> inputs of the Shannon's derived channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$M$</tex></formula></emphasis>-ary signal transmission for the additive white Gaussian noise (AWGN) channel with additive <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula></emphasis>-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 <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\log_2 M$</tex></formula></emphasis> is achievable by a one-shot coding scheme if <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">${\cal X}$</tex></formula></emphasis> is an arithmetic progression. </para>
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".