Rank deficient decoding for arithmetic subspace network coding
Bibliographic record
Abstract
In arithmetic network coding (ANC), finite field operations are replaced by real or complex arithmetic operations. This has applications in physical layer network coding or in multi-resolution multicast, where users with a higher download capacity experience a better quality of service. A major problem in random ANC is that the condition number of the network grows quickly with the network size, hence, noise can cause many errors in larger networks. An efficient solution for error correction in network coding is subspace coding. However, existing subspace coding solutions are based on finite field operations and cannot be used with ANC. Some of the difficulties of applying subspace coding to ANC are: (i) there are infinite subspaces to choose from; (ii) the effect of noise is on all links, where the noise strength increases hop by hop; and (iii) the decoding algorithms of ANC and subspace decoding are very different. In this work, we develop a subspace arithmetic network coding framework. We first model the network noise from which we then develop a decoding algorithm. Our simulation results show the success of our proposed method over conventional ANC.
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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 | 0.001 | 0.005 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".