How Suboptimal Is the Shannon Code?
Bibliographic record
Abstract
In order to determine how suboptimal the Shannon code is, one should compare its performance with that of the optimal code, i.e., the corresponding Huffman code, in some sense. It is well known that in the worst case the redundancy of both the Shannon and Huffman codes can be arbitrarily close to 1. Beyond this worst case viewpoint, very little is known. In this paper, we compare the performance of these codes from an average point of view. The redundancy is considered as a random variable on the set of all sources with n symbols and its average is evaluated. It is shown that the average redundancy of the Shannon code is very close to 0.5 bits, whereas the average redundancy of the Huffman code is less than n-1(1+ln n)+0.086 bits . It is also proven that the variance of the redundancy of the Shannon code tends to zero as n increases. Therefore, for sources with alphabet size n, the redundancy of the Shannon code is approximately 0.5 bits with probability approaching 1 as n→ ∞.
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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 | 0.007 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".