On the Fundamental Limits of Integrated Sensing and Communications Under Logarithmic Loss
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Bibliographic record
Abstract
We study a unified information-theoretic framework for integrated sensing and communications (ISAC), applicable to both monostatic and bistatic sensing scenarios. Special attention is given to the case where the sensing receiver (Rx) is required to produce a “soft" estimate of the state sequence, with logarithmic loss serving as the performance metric. We derive lower and upper bounds on the capacity-distortion function, which delineates the fundamental tradeoff between communication rate and sensing distortion. These bounds coincide when the channel between the ISAC transmitter (Tx) and the communication Rx is degraded with respect to the channel between the ISAC Tx and the sensing Rx, or vice versa. Furthermore, we provide a complete characterization of the capacity-distortion function for an ISAC system that simultaneously transmits information over a binary-symmetric channel and senses additive Bernoulli states through another binary-symmetric channel. The Gaussian counterpart of this problem is also explored, which, together with a state-splitting trick, fully determines the capacity-distortion-power function under the squared error distortion measure.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| 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 it