Robust capacity of white Gaussian noise channels with uncertainty
Bibliographic record
Abstract
This paper concerns the problem of defining, and computing the channel capacity of a continuous time additive white Gaussian noise channel when the true frequency response of the channel is not completely known to the transmitter, and receiver, and when a transmitted signal is a wide sense stationary process constrained in power. To represent the uncertainty of a true frequency response two basic uncertainty models are used that are borrowed from the control theory. additive; and multiplicative. Here, the true frequency response although unknown, belongs to a ball in a normed linear space. The radius of the ball is a function of frequency; and it depends on the size of the uncertainty. The channel capacity, called robust capacity is defined as a max-min of the mutual information rate, where the maximum is over all power spectral densities of the input signal with constrained power, and minimum is over the uncertainty set of frequency response. The robust capacity formula is explicitly computed describing how the channel uncertainty reduces the capacity. The water-filling formula is derived showing how the optimal transmitted power changes with uncertainty. At the end it is shown that a channel coding theorem, and its converse under certain conditions imposed on the uncertainty set hold for the robust maximum capacity.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".