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On the Polarization Levels of Automorphic-Symmetric Channels

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Rajai Nasser

Information Theory · Submitted 13 Nov 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the polarization levels of an automorphic-symmetric channel are determined by characteristic subgroups.

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arXiv ID1811.05203 (version 2)
Pith IDSOGOJP4G, Pith's permanent record of this paper and its review
CitationRajai Nasser. "On the Polarization Levels of Automorphic-Symmetric Channels." arXiv:1811.05203 (2018). https://pith.science/paper/SOGOJP4G
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,237 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.28 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.70 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

It is known that if an Abelian group operation is used in an Ar{\i}kan-style construction, we have multilevel polarization where synthetic channels can approach intermediate channels that are neither almost perfect nor almost useless. An open problem in polarization theory is to determine the polarization levels of a given channel. In this paper, we discuss the polarization levels of a family of channels that we call automorphic-symmetric channels. We show that the polarization levels of an automorphic-symmetric channel are determined by characteristic subgroups. In particular, if the group that is used does not contain any non-trivial characteristic subgroup, we only have two-level polarization to almost perfect and almost useless channels.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 It is known that if an Abelian group operation is used in an Ar{\i}kan-style construction, we have multilevel polarization where synthetic channels can approach intermediate channels that are neither almost perfect nor almost useless. background 1.00 0.04 0.03 asserted 1.00
s1 An open problem in polarization theory is to determine the polarization levels of a given channel. gap 0.94 0.03 0.02 asserted 0.99
s2 In this paper, we discuss the polarization levels of a family of channels that we call automorphic-symmetric channels. contribution 0.99 0.52 0.05 asserted 0.78
s3 We show that the polarization levels of an automorphic-symmetric channel are determined by characteristic subgroups. result 0.93 0.94 0.81 asserted 1.00
s4 In particular, if the group that is used does not contain any non-trivial characteristic subgroup, we only have two-level polarization to almost perfect and almost useless channels. result 0.98 0.88 0.30 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

It is known that if an Abelian group operation is used in an Ar{\i}kan-style construction, we have multilevel polarization where synthetic channels can approach intermediate channels that are neither almost perfect nor almost useless. An open problem in polarization theory is to determine the polarization levels of a given channel. In this paper, we discuss the polarization levels of a family of channels that we call automorphic-symmetric channels. We show that the polarization levels of an automorphic-symmetric channel are determined by characteristic subgroups. In particular, if the group that is used does not contain any non-trivial characteristic subgroup, we only have two-level polarization to almost perfect and almost useless channels.

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1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper
  • While the Arıkan-style two-by-two polar transform is always defined on a group of order two [Groups of order two are unique up to isomorphism.] in the study of binary polar codes, note that it can be defined on several binary operations in the study of non-binary polar codes. Şaşoğlu [ref] considered it based on certain finite quasigroups; Mori–Tanaka [ref] on finite fields; Park–Barg [ref] on cyclic groups in which those orders are a power of two; Sahebi–Pradhan [ref] on finite abelian groups; Nasser–Telatar [ref] on finite quasigroups; Nasser–Telatar [ref] also on finite abelian groups; Nasser [ref] on more weaker finite algebras than quasigroups; Nasser [ref] also on finite, not necessarily abelian, groups; and the authors [ref] on finite cyclic groups.

    Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions · Binary Operation defining Polar Transform · 0.92

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