Bounds on the Capacity of Discrete Memoryless Channels Corrupted by Synchronization and Substitution Errors
Bibliographic record
Abstract
We study the capacity of discrete memoryless channels with synchronization errors and additive noise. We first show that with very large alphabets, their capacity can be achieved by independent and identically distributed input sources, and establish proven tight lower and upper capacity bounds. We also derive tight numerical capacity bounds for channels where the synchronization between the input and output is partly preserved, for instance using incorruptible synchronization markers. Such channels include channels with duplication errors, channels that only insert or delete zeros, and channels with bitshift errors studied in magnetic recording. Channels with small alphabets and corrupted by synchronization errors have an infinite memory. Revisiting the theoretical work of Dobrushin and adapting techniques used to compute capacity bounds for finite-state source/channel models, we compute improved numerical capacity lower bounds for discrete memoryless channels with small alphabets, synchronization errors, and memoryless noise. An interesting and some- what surprising result is that as long as the input sequences are not completely deleted, the capacity of channels corrupted by discrete timing errors is always nonzero even if all the symbols are corrupted.
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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 | 0.003 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".