A Neural Network Implementation Of A Permutation Decoder For Binary Cyclic Codes
Bibliographic record
Abstract
In this paper we consider the decoding of binary cyclic block codes utilizing a permutation decoding technique based on a Hopfield type neural network architecture. It is well known that the maximum likelihood decoding of an $ n,k,t) :: binary hear code is equivalent to finding the minimum of a polynomial orm in k blnary vambles [ 11, (31. Using results from the work of Baldi [2], we show that a generalized Hopfield neural 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? or fewer errors are introduced in the transmission process. An energy function is defined and is the basis of the updating of the network operating in serial mode. It is shown that changes to the state of the network based on a local improvement algorithm results in a lowering of the corresponding energy of the network and hence a descent in the energy space towards the codeword. If the codeword corresponding to the state of the network is within the Hamming energy sphere of the received word, then successful decoding has been achieved otherwise a permutation is applied to the received word and the process is repeated. This provides a useful mechanism for handling the local minimum problem which plagues optimization problems. We discuss the conditions under which the state will converge to the right codeword in the presence of random errors. We present a detailed algorithm for updating the state of the network and simulation results for non-trivial cyclic codes such as the (63,30,6) and (127,64,10) BCH codes. Summan,
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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 | 0.001 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".