On the automorphism group of polar codes

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Web20 de jul. de 2024 · Abstract: Polar codes are the first class of channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels (B-DMC) with … WebMathematician/Senior Research Engineer at Dr. Vladimir Ivanov Coding Competence Center. Huawei Technologies. окт. 2024 – май 20248 месяцев. Moscow. I am Applied Mathematician/Software Engineer who together with my team members invent and/or construct algorithms for ABC - Codes and Soft decoders (Code on the Graph): A.

The Complete Affine Automorphism Group of Polar Codes

Web25 de jan. de 2024 · Abstract: In this paper, we propose an analysis of the automorphism group of polar codes, with the aim of designing codes tailored for automorphism ensemble (AE) decoding. Using a novel description of polar codes as monomial codes through negative monomials, we prove the equivalence between the notion of … Web21 de out. de 2024 · In this paper we deal with polar code automorphisms that are beneficial under low-latency automorphism ensemble (AE) decoding, and we propose polar code designs that have such automorphisms. Successive-cancellation (SC) decoding and thus SC-based AE decoding are invariant with respect to the only known polar code … photo monuments

On the Automorphism Group of Polar Codes - NASA/ADS

Web16 de jan. de 2024 · DOI: 10.1109/REDUNDANCY48165.2024.9003333 Corpus ID: 58014122; Permutation Decoding of Polar Codes @article{Kamenev2024PermutationDO, title={Permutation Decoding of Polar Codes}, author={Mikhail Kamenev and Yulia Kameneva and Oleg F. Kurmaev and Alexey Maevskiy}, journal={2024 XVI International … WebPolar codes have been recently shown to have an automorphism group larger than the lower-triangular affine group. Permutations from this group can be used in an automorphism successive cancellation (SC) decoding algorithm providing a lower latency compared to that of successive cancellation list decoding. In this paper, we demonstrate … WebIn this paper we deal with polar code automorphisms that are beneficial under low-latency automorphism ensemble (AE) decoding, and we propose polar code designs that have such automorphisms. Successive-cancellation (SC) decoding and thus SC-based AE decoding are invariant with respect to the only known polar code automorphisms, … how does inheritance work in javascript

Classification of Automorphisms for the Decoding of Polar Codes

The Complete SC-Invariant Afﬁne Automorphisms of Polar Codes

Web24 de jan. de 2024 · Upload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). Web1 de dez. de 2024 · The variables in (1) are the binary representations of code bit indices, and thus affine transformations represent code bit permutations. The automorphism … photo morestelWebas automorphism ensemble (AE) decoding. Lower-triangular afﬁne (LTA) transformations form a sub-group of the automorphism group of polar codes [9]. However, these transformations commute with SC decoding [8], leading to no gain under AE decoding. In [10], [11], the block-lower-triangular afﬁne (BLTA) group was proved to be the photo moorea

"Web26 de jun. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders … " - On the automorphism group of polar codes

On the automorphism group of polar codes

The Complete Affine Automorphism Group of Polar Codes

WebHowever, 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.

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Web26 de mar. de 2024 · However, the PSC framework is ineffective for permutations falling into the lower-triangular affine (LTA) automorphism group, as they are invariant under SC … Web21 de fev. de 2024 · The automorphism groups of the Reed-Muller and eBCH codes limit the efficiency of their polar-like decoding for long codes, hence we either should focus on short lengths or find another way. We demonstrate that asymptotically same restrictions (although with a slower convergence) hold for more relaxed condition that we call partial …

Web24 de jan. de 2024 · For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial … Web17 de out. de 2024 · In [10], [11], the blocklower-triangular affine (BLTA) group was proved to be the complete affine automorphism group of a polar code. In [10], [12] , BLTA transformations were successfully applied ...

Web27 de out. de 2024 · Our proposal permits to design a polar code with the desired automorphism group (if possible) while assuring the decreasing monomial property. Moreover, we prove that some automorphisms are redundant under AE decoding, and we propose a new automorphisms classification based on equivalence classes. Web7 de jun. de 2024 · In this paper, we propose an analysis of the automorphism group of polar codes, with the scope of designing codes tailored for automorphism ensemble (AE) decoding. We prove the equivalence between the notion of decreasing monomial codes and the universal partial order (UPO) framework for the description of polar codes.

Web12 de jul. de 2024 · In [13], [14], the complete affine automorphisms group of a polar code is proved to be the block-lower-triangular affine (BLTA) group. Authors in [12], [13] …

Web7 de jun. de 2024 · In this paper, we propose an analysis of the automorphism group of polar codes, with the scope of designing codes tailored for automorphism ensemble … how does inheritance work ukWeb23 de mar. de 2024 · 1. Introduction. There have been many recent advancements in the categorical approach toward probability theory and statistics. For example, the Kolmogorov zero-one law, Basu’s theorem, Fisher–Neymann factorization, de Finetti’s theorem, the d-separation criterion and the ergodic decomposition theorem have all been proved … photo moorhenWeb27 de out. de 2024 · This paper proposes new polar code design principles for the low-latency automorphism ensemble (AE) decoding. Our proposal permits to design a polar code with the desired automorphism group (if ... how does inheritance tax work irelandWebresearchmapは、日本の研究者情報を収集・公開するとともに、研究者等による情報発信の場や研究者等の間の情報交換の場を提供することを目的として、国立研究開発法人科学技術振興機構（JST）が運営するサービスです。 photo more than 100 kbWebThe automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism … how does inheriting a house affect taxesWeb16 de fev. de 2024 · automorphism group of polar codes [12], researchers used this. group under AE decoding; however, SC decoding was proved. to be invariant under L T A automorphisms, and SC-based AE. photo morganeWeb27 de out. de 2024 · This paper proposes new polar code design principles for the low-latency automorphism ensemble (AE) decoding. Our proposal permits to design a polar … photo mordred