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On the automorphism group of polar codes

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 … 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, …

Group Properties of Polar Codes for Automorphism Ensemble …

Web27 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 ... Web9 de mai. de 2024 · The variables in (4) are the binary representations of code bit indices, and thus affine transformations represent code bit permutations. The automorphism group of any R (r, n) Reed-Muller code is known to be the complete affine group G A (n) [WilliamsSloane], while the affine automorphism group of polar codes is the block … the ponytail project https://letmycookingtalk.com

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Web《Hadronic Journal》共发表177篇文献，掌桥科研收录2004年以来所有《Hadronic Journal》期刊内所有文献， ISSN为0162-5519， Webparameter, polar codes will be decreasing monomial codes [6], [12]. In this way, polar codes can be generated by I min, where the information set is the smallest decreasing set containing I min. From now on, we always suppose Iis decreasing. B. Affine automorphism group Let C be a decreasing monomial code with length n. A 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 … sidley events

The Complete Affine Automorphism Group of Polar Codes

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On the automorphism group of polar codes

Hadronic Journal -外文期刊【掌桥科研】

Web23 de dez. de 2024 · In this paper, we prove that Arikan’s polar codes in fact cannot have many useful permutations in their automorphism group. This result is a direct consequence of the recent characterization of the automorphism groups of decreasing monomial codes [ 10 ] which we plug into the framework of partial symmetry [ 7 , 8 ] . WebThe 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 …

On the automorphism group of polar codes

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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. 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 …

Web16 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. Web25 de mar. de 2024 · Related works on automorphism group of RM and Polar codes. In this paper, we prove that for decreasing codes, per-arXiv:2103.14215v1 [cs.IT] 26 Mar 2024.

WebThis article is published in Proceedings of The London Mathematical Society.The article was published on 1978-07-01. It has received 29 citation(s) till now. The article focuses on the topic(s): Frobenius group & Sylow theorems. WebThe 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 group …

WebExample: Some belief-propagation decoder of polar codes uses the Aut of RM codes (not the Aut of polar codes) to permute the Tanner graph. It is easier to analyze the code … sidley facebookWebHowever, 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. sidley peopleWeb20 de jul. de 2024 · The 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 … sidle of csiWeb25 de mar. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders … theponytaleWebThe main code is contained in the files: CodeEnv.py: environment class based on OpenAI Gym; utils.py: various helper functions (mainly to implement the permutation preprocessing based on the code's automorphism group) The actual optimization uses RLlib and Tune, both of which are based on Ray. Workflow 0) Initialization sidley diamondWeb7 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 … the pony tails born too lateWebAbstract—The 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 … the pony who couldn\u0027t say neigh