On the automorphism group of polar codes
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 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 …
On the automorphism group of polar codes
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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 … 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 …
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 …
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 … 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 …
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 … how do people catch the fluWebAs 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 ... how do people cause air pollutionWeb20 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 … how do people cause weatheringWeb23 de mar. de 2024 · 1. Introduction. There have been many recent advancements in the categorical approach toward probability theory and statistics. For example, the Kolmogorov zero-one law, Basu’s theorem, Fisher–Neymann factorization, de Finetti’s theorem, the d-separation criterion and the ergodic decomposition theorem have all been proved … how do people celebrate all saints dayWebHowever, 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. how much protein should we consume dailyWeb25 de mar. de 2024 · Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders … how much protein should you consume each dayWeb16 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. how do people celebrate birthdays in china