A Multi-Kernel Multi-Code Polar Decoder Architecture
Bibliographic record
Abstract
Polar codes have received increasing attention in the past decade, and have been selected for the next generation of the wireless communication standard. Most research on polar codes has focused on codes constructed from a 2×2 polarization matrix, called binary kernel: codes constructed from binary kernels have code lengths that are bound to powers of 2. A few recent works have proposed construction methods based on multiple kernels of different dimensions, not only binary ones, allowing code lengths different from powers of 2. In this paper, we design and implement the first multi-kernel successive cancellation polar code decoder in literature. It can decode any code constructed with binary and ternary kernels: the architecture, sized for a maximum code length N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> , is fully flexible in terms of code length, code rate, and kernel sequence. The decoder can achieve a frequency of over 1 GHz in 65 nm CMOS technology, and a throughput of 615 Mb/s. The area occupation ranges between 0.11 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> = 256 and 2.01 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> = 4096. Implementation results show an unprecedented degree of flexibility: with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> = 4096, up to 55 code lengths can be decoded with the same hardware, along with any kernel sequence and code rate.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".