Bibliographic record
Abstract
It is well known that the maximum likelihood decoding of a binary (n,k,d) code is equivalent to finding the maxima (minima) of a polynomial form in k binary variables. We extend this method to the problem of permutation decoding of binary cyclic codes and give an implementation based on a Hopfield type neural network architecture. Using results from Baldi (1988), we show that a generalized Hopfield network whose connections are governed by the generator matrix of the code and the received word has a stable state corresponding to the transmitted codeword if t=[(d-1)/2] or fewer errors are introduced in the transmission process. An energy function is defined and the search for a global maxima is done through a selective updating of neurons( information bits). The value of the energy function call be related to the Hamming distance of the received word and to the codeword corresponding to the current state of the network so that if we come within the Hamming sphere of a codeword, successful decoding has been achieved. By utilizing the known permutation group of the code, the local maxima problem which plagues all optimization search is alleviated. We discuss the conditions under which the network will converge to the right codeword in the presence of random errors as well as various updating algorithms. Finally we conclude with simulation results for non-trivial cyclic codes such as the (63,30,13), the (127,64,2) and the (255,131,37) BCH codes using different approaches to searching the energy space.>
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".