Decoding of Polar Codes Using Quadratic Unconstrained Binary Optimization
Bibliographic record
Abstract
Polar codes encounter challenges in decoder complexity while preserving good error-correction properties. Instead of conventional decoders, a quantum annealer (QA) decoder has been proposed to explore untapped possibilities. For future QA applications, a crucial prerequisite is transforming the optimization problem into quadratic unconstrained binary optimization (QUBO) form. However, existing QUBO forms for polar decoding result in suboptimal frame error rate (FER) performance for codes exceeding 8 bits. This paper redesigns the QUBO form for polar decoding. We first introduce a novel receiver constraint modeled by the binary cross-entropy (BCE) function. Utilizing a simulated annealing (SA) solver with the proposed QUBO form with BCE (QUBO-BCE) achieves maximum-likelihood (ML) performance for a code length of 32 bits. Next, to reduce the number of variables, we remove the frozen variables and introduce a simplified QUBO-BCE form (SQUBO-BCE). Additionally, CRC polynomials are modelled into constraints in QUBO form, resulting in a CRC-aided SQUBO-BCE (CA-SQUBO-BCE) form for polar decoding to further enhance the FER. Numerical results demonstrate that SQUBO-BCE achieves ML performance and reduces up to 61.5% of variables compared to QUBO-BCE. Furthermore, the proposed CA-SQUBO-BCE achieves near CRC-aided ML performance. The proposed SQUBO-BCE requires the lowest number of SA processes to reach a specific FER.
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 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 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| 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 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".