Codebook information does not reduce output entropy when rate is above capacity
Bibliographic record
Abstract
Under the standard random coding framework, the conditional entropy rate of the channel output given the codebook information is investigated. It is shown that there exists an interesting dichotomy: with respect to the unconditional entropy rate of the output, this conditional entropy rate is reduced when the communication rate is below the channel capacity, but remains the same when the communication rate is above the channel capacity. Hence, the channel capacity plays a role of the critical point. Shannon used the random codebook argument to prove that any communication rate below the channel capacity is achievable, i.e., the destination can successfully decode the transmitted codeword based on the codebook used at the source. However, this cannot be done when the communication rate is above the channel capacity. In this case, our evaluation shows that the codebook information cannot be used to reduce the output entropy rate, and instead, the output entropy rate turns to be the same as if a completely random, instead of a specific codebook, was used at the source. This characterization of the conditional entropy rate sheds some light on the optimal design of the compress-and-forward relay schemes, where a long standing question is whether the source's codebook information can be used for more effective compressions at the relay. In this paper, specifically, we show that if lossless compression is to be performed, then the codebook information cannot be used to reduce the compression rate at the relay.
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 | 0.004 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 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".