Minimal Sets for Capacity-Approaching Variable-Length Constrained Sequence Codes
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Bibliographic record
Abstract
The use of constrained sequence (CS) codes is important for the robust operation of transmission and data storage systems. While most analysis and development of CS codes have focused on fixed-length codes, recent research has demonstrated the advantages of variable-length CS codes. In our design of capacity-approaching variable-length CS codes, the construction of minimal sets is critical. In this paper, we propose an approach to construct minimal sets for a variety of constraints based on the finite-state machine (FSM) description of CSs. We develop three criteria to select the optimal state of the FSM that enables the design of a single-state encoder that results in the highest maximum possible code rate, and we apply these criteria to several constraints to illustrate the advantages that can be achieved. We then introduce FSM partitions and propose a recursive construction algorithm to establish the minimal set of the specified state. Finally, we present the construction of single-state capacity-approaching variable-length CS codes to show the improved efficiency and reduced implementation complexity that can be achieved compared with CS codes currently in use.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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