  Typical performance of low-density parity-check (LDPC) codes over a general
binary-input output-symmetric memoryless channel is investigated using methods
of statistical mechanics. Theoretical framework for dealing with general
symmetric channels is provided, based on which Gallager and MacKay-Neal codes
are studied as examples of LDPC codes. It has been shown that the basic
properties of these codes known for particular channels, including the property
to potentially saturate Shannon's limit, hold for general symmetric channels.
The binary-input additive-white-Gaussian-noise channel and the binary-input
Laplace channel are considered as specific channel noise models.
