On the automorphism group of polar codes

WebAs decreasing monomial codes, polar codes have a large automorphism group. It is first shown in [13] that the auto-mophism group of decreasing monomial codes includes the lower triangular affine group (LTA). Recently in [20], this result has been extended to the block lower triangular affine group (BLTA). Later in [21], it has also been ... Webof 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 …

Polar Codes for Automorphism Ensemble Decoding - IEEE Xplore

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 … 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 ... chinese stonehaven https://urlinkz.net

On the Automorphism Group of Polar Codes Papers With Code

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] … 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 … 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 ] . grandview cattle

The Complete Affine Automorphism Group of Polar Codes

Category:Group Properties of Polar Codes for Automorphism Ensemble …

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On the automorphism group of polar codes

On the Automorphism Group of Polar Codes

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. 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 …

On the automorphism group of polar codes

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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 … Web20 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 …

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. 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，

WebRecently, 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 … 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 …

Web25 de mar. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders …

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 … chinese stomach ache pillsWeb25 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. grandview cattle feeders picture butteWeb24 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). chinese stomach cancerWebIn 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, … chinese stomach workoutWebThe 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 chinese stonehaven brickfieldWeb20 de jul. 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 … chinese stonehouseWebThe 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 … grandview ccsd