  In previous work, an ordering result was given for the symbolwise probability
of error using general Markov channels, under iterative decoding of LDPC codes.
In this paper, the ordering result is extended to mutual information, under the
assumption of an iid input distribution. For certain channels, in which the
capacity-achieving input distribution is iid, this allows ordering of the
channels by capacity. The complexity of analyzing general Markov channels is
mitigated by this ordering, since it is possible to immediately determine that
a wide class of channels, with different numbers of states, has a smaller
mutual information than a given channel.
