Advances in Neural Information Processing Systems, pp. 527–534

著者:

  • Toshiyuki Tanaka
  • Shiro Ikeda
  • Shun-ichi Amari

URL:

Abstract:

We report a result of perturbation analysis on decoding error of the belief propagation decoder for Gallager code. The analysis is based on information geometry, and it shows that the principal term of decoding error at equilibrium comes from the m-embedding curvature of the log-linear submanifold spanned by the estimated pseudoposteriors, one for the full marginal, and K for the posteriors with single checks, where K is the number of checks in the Gallager code. It is then shown that the principal error term vanishes when the parity-check matrix of the code is so sparse that there are no two columns with overlap greater than 1.