  Low-density parity-check (LDPC) coding for a multitude of equal-capacity
channels is studied. First, based on numerous observations, a conjecture is
stated that when the belief propagation decoder converges on a set of
equal-capacity channels, it would also converge on any convex combination of
those channels. Then, it is proved that when the stability condition is
satisfied for a number of channels, it is also satisfied for any channel in
their convex hull. For the purpose of code design, a method is proposed which
can decompose every symmetric channel with capacity C into a set of
identical-capacity basis channels. We expect codes that work on the basis
channels to be suitable for any channel with capacity C. Such codes are found
and in comparison with existing LDPC codes that are designed for specific
channels, our codes obtain considerable coding gains when used across a
multitude of channels.
