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On the Concavity of Auxiliary Function in Classical-Quantum Channels
Journal
IEEE Trans. Inf. Theory, 62(10), 5960 - 5965, 2016
Journal Volume
62
Journal Issue
10
Pages
5960
End Page
5965
Date Issued
2016-02-10
Author(s)
Min-Hsiu Hsieh
Abstract
The auxiliary function of a classical channel appears in two fundamental
quantities that upper and lower bound the error probability, respectively. A
crucial property of the auxiliary function is its concavity, which leads to
several important results in finite block length analysis. In this paper, we
prove that the auxiliary function of a classical-quantum channel also enjoys
the same concave property, extending an earlier partial result to its full
generality. The key component in our proof is a beautiful result of geometric
means of operators.
quantities that upper and lower bound the error probability, respectively. A
crucial property of the auxiliary function is its concavity, which leads to
several important results in finite block length analysis. In this paper, we
prove that the auxiliary function of a classical-quantum channel also enjoys
the same concave property, extending an earlier partial result to its full
generality. The key component in our proof is a beautiful result of geometric
means of operators.
Subjects
Auxiliary function; classical-quantum channel; matrix geometric mean; reliability function; sphere-packing bound; LOWER BOUNDS; INEQUALITIES; PROBABILITY; ERROR; TRACE; Quantum Physics; Quantum Physics; Computer Science - Information Theory; Mathematics - Information Theory
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Type
journal article