  The error exponent of Markov channels with feedback is studied in the
variable-length block-coding setting. Burnashev's classic result is extended
and a single letter characterization for the reliability function of
finite-state Markov channels is presented, under the assumption that the
channel state is causally observed both at the transmitter and at the receiver
side. Tools from stochastic control theory are used in order to treat channels
with intersymbol interference. In particular the convex analytical approach to
Markov decision processes is adopted to handle problems with stopping time
horizons arising from variable-length coding schemes.
