The Complete Affine Automorphism Group of Polar Codes Article Swipe
Yuan Li
,
Huazi Zhang
,
Rong Li
,
Jun Wang
,
Wen Tong
,
Guiying Yan
,
Zhi-Ming Ma
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2103.14215
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2103.14215
Recently, a permutation-based successive cancellation (PSC) decoding framework for polar codes attaches much attention. It decodes several permuted codewords with independent successive cancellation (SC) decoders. Its latency thus can be reduced to that of SC decoding. However, the PSC framework is ineffective for permutations falling into the lower-triangular affine (LTA) automorphism group, as they are invariant under SC decoding. As such, a larger block lower-triangular affine (BLTA) group that contains SC-variant permutations was discovered for decreasing polar codes. But it was unknown whether BLTA equals the complete automorphism group. In this paper, we prove that BLTA equals the complete automorphisms of decreasing polar codes that can be formulated as affine trasformations.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2103.14215
- https://arxiv.org/pdf/2103.14215
- OA Status
- green
- Cited By
- 2
- References
- 20
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3147906298
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https://openalex.org/W3147906298Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2103.14215Digital Object Identifier
- Title
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The Complete Affine Automorphism Group of Polar CodesWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-03-26Full publication date if available
- Authors
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Yuan Li, Huazi Zhang, Rong Li, Jun Wang, Wen Tong, Guiying Yan, Zhi-Ming MaList of authors in order
- Landing page
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https://arxiv.org/abs/2103.14215Publisher landing page
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https://arxiv.org/pdf/2103.14215Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2103.14215Direct OA link when available
- Concepts
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Mathematics, Affine transformation, Automorphism group, Decoding methods, Automorphism, Combinatorics, Polar, Invariant (physics), Permutation (music), Discrete mathematics, Affine group, Block (permutation group theory), Algorithm, Pure mathematics, Physics, Acoustics, Mathematical physics, AstronomyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
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2022: 1, 2021: 1Per-year citation counts (last 5 years)
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20Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.group. | 88 |
| abstract_inverted_index.larger | 62 |
| abstract_inverted_index.paper, | 91 |
| abstract_inverted_index.decodes | 15 |
| abstract_inverted_index.falling | 44 |
| abstract_inverted_index.latency | 26 |
| abstract_inverted_index.reduced | 30 |
| abstract_inverted_index.several | 16 |
| abstract_inverted_index.unknown | 81 |
| abstract_inverted_index.whether | 82 |
| abstract_inverted_index.However, | 36 |
| abstract_inverted_index.attaches | 11 |
| abstract_inverted_index.complete | 86, 98 |
| abstract_inverted_index.contains | 69 |
| abstract_inverted_index.decoding | 6 |
| abstract_inverted_index.permuted | 17 |
| abstract_inverted_index.Recently, | 0 |
| abstract_inverted_index.codewords | 18 |
| abstract_inverted_index.decoders. | 24 |
| abstract_inverted_index.decoding. | 35, 58 |
| abstract_inverted_index.framework | 7, 39 |
| abstract_inverted_index.invariant | 55 |
| abstract_inverted_index.SC-variant | 70 |
| abstract_inverted_index.attention. | 13 |
| abstract_inverted_index.decreasing | 75, 101 |
| abstract_inverted_index.discovered | 73 |
| abstract_inverted_index.formulated | 107 |
| abstract_inverted_index.successive | 3, 21 |
| abstract_inverted_index.independent | 20 |
| abstract_inverted_index.ineffective | 41 |
| abstract_inverted_index.automorphism | 50, 87 |
| abstract_inverted_index.cancellation | 4, 22 |
| abstract_inverted_index.permutations | 43, 71 |
| abstract_inverted_index.automorphisms | 99 |
| abstract_inverted_index.trasformations. | 110 |
| abstract_inverted_index.lower-triangular | 47, 64 |
| abstract_inverted_index.permutation-based | 2 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 7 |
| citation_normalized_percentile |