Asymmetric Construction of Low-Latency and Length-Flexible Polar Codes
Why this work is in the frame
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Bibliographic record
Abstract
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> generation (5G) wireless standard. Most polar code research examines the original Arkan polar coding scheme, which is limited in block length to powers of two. This constraint presents a considerable obstacle since practical applications call for all code lengths to be readily available. Puncturing and shortening techniques allow for flexible polar codes, while multi-kernel polar codes produce native code lengths that are powers of two and or three. In this work, we propose a new low complexity coding scheme called asymmetric polar coding that allows for any arbitrary block length. We present details on the generator matrix, frozen set design, and decoding schedule. Our scheme offers flexible polar code lengths with decoding complexity lower than equivalent state-of-the-art length-compatible approaches under successive cancellation decoding. Further, asymmetric decoding complexity is directly dependent on the codeword length rather than the nearest valid polar code length. We compare our scheme with other length matching techniques, and simulations are presented. Results show that asymmetric polar codes present similar error correction performance to the competing schemes, while dividing the number of SC decoding operations by up to a factor of 2 using the same codeword length.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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 it