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- W4235589969 abstract "In [1], it was conjectured that the permanent of a P-lifting θ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>↑P</sup> of a matrix θ of degree M is less than or equal to the Mth power of the permanent perm(θ), i.e., perm(θ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>↑P</sup> ) ≤ perm(θ) <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>M</sup> and, consequently, that the degree-M Bethe permanent perm <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>M,B</sub> (θ) of a matrix θ is less than or equal to the permanent perm(θ) of θ, i.e., perm <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>M,B</sub> (θ) ≤ perm(θ). In this paper, we prove these related conjectures and show some properties of the permanent of block matrices that are lifts of a matrix. As a corollary, we obtain an alternative proof of the inequality perm <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>B</sub> (θ) ≤ perm(θ) on the Bethe permanent of the base matrix θ, which, in contrast to the one given in [2], uses only the combinatorial definition of the Bethe-permanent. The results have implications in coding theory. Since a P-lifting corresponds to an M-graph cover and thus to a protograph-based LDPC code, the results may help explain the performance of these codes." @default.
- W4235589969 created "2022-05-12" @default.
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- W4235589969 date "2014-12-01" @default.
- W4235589969 modified "2023-09-25" @default.
- W4235589969 title "Bethe and M-Bethe Permanent Inequalities" @default.
- W4235589969 doi "https://doi.org/10.1109/glocom.2014.7417452" @default.
- W4235589969 hasPublicationYear "2014" @default.
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