On the automorphism group 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 … Webas 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
On the automorphism group of polar codes
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Web2101.09679 - Free download as PDF File (.pdf), Text File (.txt) or read online for free. WebPolar Codes for Automorphism Ensemble Decoding @article{Pillet2024PolarCF, title={Polar Codes for Automorphism Ensemble Decoding}, author={Charles Pillet and Valerio Bioglio and Ingmar Land}, journal={2024 IEEE Information Theory Workshop (ITW)}, year={2024}, pages={1-6} } Charles Pillet, V. Bioglio, I. Land; Published 16 February 2024
WebThree-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 … 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 ...
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 … 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 …
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 …
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, … ct beach passWeb25 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 … earrings with flat postWebHowever, 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. earrings with diamonds and pearlsWeb26 de jun. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders … earrings with glass beadsWeb7 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 … earrings with flat backsWeb9 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 … ct beach state parksWeb16 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 … ct beach houses for rent