  This paper proposes a practical successive decoding scheme with finite levels
for the finite-state Markov channels where there is no a priori state
information at the transmitter or the receiver. The design employs either a
random interleaver or a deterministic interleaver with an irregular pattern and
an optional iterative estimation and decoding procedure within each level. The
interleaver design criteria may be the achievable rate or the extrinsic
information transfer (EXIT) chart, depending on the receiver type. For random
interleavers, the optimization problem is solved efficiently using a
pilot-utility function, while for deterministic interleavers, a good
construction is given using empirical rules. Simulation results demonstrate
that the new successive decoding scheme combined with irregular low-density
parity-check codes can approach the identically and uniformly distributed
(i.u.d.) input capacity on the Markov-fading channel using only a few levels.
