On the automorphism group of polar codes

Author: ivna

August undefined, 2024

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 … 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 …

A Deterministic Algorithm for Computing the Weight Distribution …

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. 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 … curly mermaid sanctuary point

Group Properties of Polar Codes for Automorphism Ensemble …

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, … 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 ... 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 … curly mesh wreath tutorial

Polar Codes for Automorphism Ensemble Decoding

Classification of Automorphisms for the Decoding of Polar Codes

WebThe 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 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 curly messy bob haircutsWeb23 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 ] . curly messy bun svg

"Web25 de mar. 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

Web26 de jun. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders … 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] …

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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 … 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 …

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， 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 ...

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 … 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 …

Web24 de jan. de 2024 · Abstract: 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 …

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 … curly messy hairWebof the polar code factor graph, decoders using the concept of factor graph permutations are proposed in [4], [5] and [6]. A different approach is to use the symmetries in the code … curly messy hair drawingWebHowever, 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. curly messy hair boysWeb11 de dez. de 2024 · The Complete Affine Automorphism Group of Polar Codes Abstract: Recently, a permutation-based successive cancellation (PSC) decoding framework … curly messy hairstyles for menWeb25 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. curly messy hair menWebMathematician/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. curly method packWebThe 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 … curly method botticelli