H. J. Kappen and W. J. Wiegerinck, "Mean field theory for graphical models," in M. Opper and D. Saad (eds.), Advanced Mean Field Methods --- Theory and Practice, The MIT Press, 2001, pp. 37--49. Home/Search Document Details and Download
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Information-Geometrical Significance of Sparsity in Gallager.. - Tanaka, Ikeda (2001) (Correct)
....the design of the code, that is, the choice of the parity check matrix A. Explicit evaluation of the principal error term, as in Theorem 1, makes it possible to improve the performance of a code, just in the same way as the perturbational approach to improving the naive mean field approximation [10, 11, 12, 13, 14, 15, 16, 17]. It is believed [3] that Gallager codes have smaller average probability of decoding error if we avoid any two columns of the parity check matrix A to have overlap greater than 1. An intuitive explanation to this belief is that such avoidance prevents loops with length 4 from appearing in the ....
H. J. Kappen and W. J. Wiegerinck, "Mean field theory for graphical models," in M. Opper and D. Saad (eds.), Advanced Mean Field Methods --- Theory and Practice, The MIT Press, 2001, pp. 37--49.
Belief propagation and turbo code: Information geometrical view - Ikeda, Tanaka, Amari (2001) (Correct)
.... ) M 0 M 1 M 2 p0(x; p1(x; 2 ) p2(x; 1 ) p(xj x; y1 y2 ) Figure 4: M(# # ) and E(# # ) of turbo decoding is a discrepancy between M(# # ) and E(# # ) Therefore q(x) is not necessarily included in M(# # ) The similar structure exists in some problems in statistical physics[2, 6, 10] 5. Information geometrical analysis 5.1. Local stability analysis We show the condition for the equilibrium point to be stable. Equation (12) is rewritten as follows with #, # 0 (# # ) # 1 (# # 2 ) # 2 (# # 1 ) For the following discussion, we define the Fisher information matrices of the ....
H. J. Kappen and W. J. Wiegerinck. Mean field theory for graphical models. In M. Opper and D. Saad, editors, Adavanced Mean Field Theory -- Theory and Practice, chapter 4, pages 37--49. MIT Press, 2001.
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