  ``Nishimori line'' is a line or hypersurface in the parameter space of
systems with quenched disorder, where simple expressions of the averages of
physical quantities over the quenched random variables are obtained. It has
been playing an important role in the theoretical studies of the random
frustrated systems since its discovery around 1980. In this paper, a novel
interpretation of the Nishimori line from the viewpoint of statistical
information processing is presented. Our main aim is the reconstruction of the
whole theory of the Nishimori line from the viewpoint of Bayesian statistics,
or, almost equivalently, from the viewpoint of the theory of error-correcting
codes. As a byproduct of our interpretation, counterparts of the Nishimori line
in models without gauge invariance are given. We also discussed the issues on
the ``finite temperature decoding'' of error-correcting codes in connection
with our theme and clarify the role of gauge invariance in this topic.
