A Hybrid Reliability--Weight Framework for Construction of Polar Codes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912831538987008 |
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| author | Rowshan, Mohammad Dragoi, Vlad-Florin |
| author_facet | Rowshan, Mohammad Dragoi, Vlad-Florin |
| contents | Polar codes are usually constructed by ranking synthetic bit-channels according to reliability, which guarantees capacity-achieving behavior but can yield poor low-weight spectra at short and moderate lengths. Recent algebraic results express the contribution of individual bit-channels to the multiplicities of minimum and near-minimum weight codewords in closed form. In this work we combine these insights into a mixed (reliability--weight) bit-channel ordering. We define a per-bit cost whose distance term is derived from orbit enumeration of minimum-weight codewords and scaled by a Bhattacharyya-type factor, and show that the resulting mixed construction minimises a truncated SC/ML union-bound surrogate within a class of decreasing monomial codes. We relate the mixed metric to error events in SCL decoding via a pruning/ML decomposition, and prove that mixed designs act as local perturbations of reliability-based constructions whose asymptotic impact vanishes as code-length approaches infinity. Numerical results for short and moderate lengths on BPSK-AWGN, implemented via Gaussian approximation and closed-form weight contributions, illustrate the trade-off between pure reliability-based and mixed constructions in terms of minimum distance, multiplicity, and union-bound approximations. All proofs are deferred to the appendices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10376 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Hybrid Reliability--Weight Framework for Construction of Polar Codes Rowshan, Mohammad Dragoi, Vlad-Florin Information Theory Polar codes are usually constructed by ranking synthetic bit-channels according to reliability, which guarantees capacity-achieving behavior but can yield poor low-weight spectra at short and moderate lengths. Recent algebraic results express the contribution of individual bit-channels to the multiplicities of minimum and near-minimum weight codewords in closed form. In this work we combine these insights into a mixed (reliability--weight) bit-channel ordering. We define a per-bit cost whose distance term is derived from orbit enumeration of minimum-weight codewords and scaled by a Bhattacharyya-type factor, and show that the resulting mixed construction minimises a truncated SC/ML union-bound surrogate within a class of decreasing monomial codes. We relate the mixed metric to error events in SCL decoding via a pruning/ML decomposition, and prove that mixed designs act as local perturbations of reliability-based constructions whose asymptotic impact vanishes as code-length approaches infinity. Numerical results for short and moderate lengths on BPSK-AWGN, implemented via Gaussian approximation and closed-form weight contributions, illustrate the trade-off between pure reliability-based and mixed constructions in terms of minimum distance, multiplicity, and union-bound approximations. All proofs are deferred to the appendices. |
| title | A Hybrid Reliability--Weight Framework for Construction of Polar Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.10376 |