Information geometry for turbo decoding

Shiro Ikeda; Toshiyuki Tanaka; Shun-ichi Amari

doi:10.1002/scj.10359

Information geometry for turbo decoding

Systems and Computers in Japan ◽

10.1002/scj.10359 ◽

2004 ◽

Vol 36 (1) ◽

pp. 79-87 ◽

Cited By ~ 1

Author(s):

Shiro Ikeda ◽

Toshiyuki Tanaka ◽

Shun-ichi Amari

Keyword(s):

Information Geometry ◽

Turbo Decoding

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Turbo decoding algorithm based on linear approximation of correction function

Journal of Computer Applications ◽

10.3724/sp.j.1087.2012.02113 ◽

2013 ◽

Vol 32 (8) ◽

pp. 2113-2115

Author(s):

Zheng LI ◽

Chun-lin SONG ◽

Yun-jie ZHAO ◽

Zhu-jia WU

Keyword(s):

Linear Approximation ◽

Correction Function ◽

Turbo Decoding ◽

Decoding Algorithm

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Quantum Orlicz Spaces in Information Geometry

Open Systems & Information Dynamics ◽

10.1007/s11080-004-6626-2 ◽

2004 ◽

Vol 11 (04) ◽

pp. 359-375 ◽

Cited By ~ 13

Author(s):

R. F. Streater

Keyword(s):

Quantum Information ◽

Tangent Space ◽

Selfadjoint Operator ◽

Affine Connection ◽

Orlicz Spaces ◽

Trace Class ◽

Information Geometry ◽

Young Function ◽

Affine Structure ◽

Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

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