Efficient encoders and decoders for polar codes: algorithms and implementations
Bibliographic record
Abstract
Error-correcting codes enable reliable and efficient data communication and storage and have become an indispensable part of information processing systems. Polar codes are the latest discovery in the quest for more powerful error correction. They are the first codes with an explicit construction to provably achieve the symmetric capacity of memoryless channels. Moreover, this performance is realizable using the low complexity successive-cancellation decoding algorithm. Despite their attractive theoretical properties, polar codes suffer from two major issues hindering practical implementations: a slow decoding algorithm and mediocre error-correction performance at moderate code lengths. Solutions to these problems in the literature have been mutually exclusive. Decoding speed can be increased, but at the cost of degrading error-correction capability. On the other hand, the error-correction performance can be greatly improved using a list decoding algorithm, which incurs a large cost in both decoding speed and memory requirements. This incompatibility in solutions must be resolved before polar codes become practical. This thesis presents novel, compatible solutions to these problems. It introduces a new decoding algorithm that has the same error-correction performance as successive cancellation, but offers significantly lower latency and higher throughput. A corresponding decoder implementation is shown to be an order of magnitude faster than the state-of-the-art in the literature. Next, the speed of successive-cancellation list decoders for polar codes is improved without degrading error-correction performance. The resulting software decoders implementing the proposed algorithm offer throughput and error-correction performance exceeding the best in the literature and meeting the requirements for the 802.11n WiFi standard. This work also brings to light another beneficial property of polar codes that had not been studied before. It presents encoders and decoders that can operate on polar codes of any length and rate, while maintaining low implementation complexity and fast operating speed. Such implementations are important in systems that must adapt to varying channel conditions. Finally, two methods are introduced that improve error-correction performance without incurring the memory overhead of list decoding. The first targets systems where re-transmission is impossible or highly undesirable. The second improves the performance of software decoders using polar codes with rates very close to the channel capacity.
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.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.004 |
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".