My recent paper in the Transactions:
A. W. Eckford, “Ordering finite-state Markov channels by mutual information,” IEEE Trans. Inform. Theory, vol. 55, no. 7, pp. 3081-3086, Jul. 2009. [PDF]
In a Markov channel, the channel parameter is selected by the state of a hidden Markov chain -- the most famous example is the Gilbert-Elliott channel, in which a channel use might see a "good" state with low crossover probability, or a "bad" state with high crossover probability.
In Gaussian noise, channels are ordered with respect to SNR -- we know that a channel with smaller SNR has smaller capacity. In this paper, I'm trying to find a similar ordering for Markov channels: the "degraded family" of a "parent" channel, where all channels in the family have smaller capacity than the parent.