On the automorphism group 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). Web24 de jan. 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 …
On the automorphism group of polar codes
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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 … 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.
Web2101.09679 - Free download as PDF File (.pdf), Text File (.txt) or read online for free. 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
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 … 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 ] .
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.
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 … inches connotationWeb25 de mar. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders … inate behaviors of chimpsWebThree-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup … inate estimating softwareWebThis 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. inatec eduWeb27 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. inches comparisonWebAbstract—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 … inate individualityWeb1 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 … inches compared to feet