Spinal Codes Optimization: Error Probability Analysis and Transmission Scheme Design.
Bibliographic record
Abstract
Spinal codes are known to be capacity achieving over both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). Over wireless channels, Spinal encoding can also be regarded as an adaptive-coded-modulation (ACM) technique due to its rateless property, which fits it with mobile communications. Due to lack of tight analysis on error probability of Spinal codes, optimization of transmission scheme using Spinal codes has not been fully explored. In this work, we firstly derive new tight upper bounds of the frame error rate (FER) of Spinal codes for both the AWGN channel and the BSC in the finite block-length (FBL) regime. Based on the derived upper bounds, we then design the optimal transmission scheme. Specifically, we formulate a rate maximization problem as a nonlinear integer programming problem, and solve it by an iterative algorithm for its dual problem. As the optimal solution exhibits an incremental-tail-transmission pattern, we propose an improved transmission scheme for Spinal codes. Moreover, we develop a bubble decoding with memory (BD-M) algorithm to reduce the decoding time complexity without loss of rate performance. The improved transmission scheme at the transmitter and the BD-M algorithm at the receiver jointly constitute an encoding-decoding system of Spinal codes. Simulation results demonstrate that it can improve both the rate performance and the decoding throughput of Spinal codes.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".