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Abstract:
We report a result of perturbation analysis on decoding error
of the belief propagation decoder for Gallager codes. 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 partial posteriors, each of which takes a single check into
account, 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.
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