Coding for Errors and Erasures in Random Network Coding
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Full frame distilled prediction
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.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Simulation or modelingConsensus signal: none
- Genre
- Candidate signal: MethodsConsensus signal: none
- Teacher disagreement score
- 0.987
- Threshold uncertainty score
- 0.486
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.227 · how far apart the two teachers sit on this one work
- Validation status
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
Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The problem of error-control in random linear network coding is considered. A “noncoherent” or “channel oblivious” model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information transmission is modeled as the injection into the network of a basis for a vector space <emphasis><formula formulatype="inline"><tex>$V$</tex></formula></emphasis> and the collection by the receiver of a basis for a vector space <emphasis><formula formulatype="inline"> <tex>$U$</tex></formula></emphasis>. A metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum-distance decoder for this metric achieves correct decoding if the dimension of the space <emphasis><formula formulatype="inline"><tex>$V \cap U$</tex></formula></emphasis> is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. Sphere-packing and sphere-covering bounds as well as a generalization of the Singleton bound are provided for such codes. Finally, a Reed–Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style “list-1” minimum-distance decoding algorithm is provided. </para>
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
The record
- Venue
- IEEE Transactions on Information Theory
- Topic
- Cooperative Communication and Network Coding
- Field
- Computer Science
- Canadian institutions
- University of Toronto
- Funders
- not available
- Keywords
- GrassmannianDecoding methodsMathematicsCode wordDiscrete mathematicsList decodingLinear network codingVector spaceCoding theoryLinear spaceLinear codeCombinatoricsAlgorithmConcatenated error correction codeBlock codeComputer scienceNetwork packetPure mathematics
- Has abstract in OpenAlex
- yes