This paper addresses the optimization of constrained stationary Markov input processes which achieve high information rates on intersymbol-interference (ISI) channels. The considered Markov processes define an optimized subset of equiprobable input symbols for each channel state and are thus uniquely described by the set of branches in a trellis section. We propose an iterative algorithm that efficiently solves the optimization problem. The algorithm successively removes the worst branches and thereby constructs a reduced trellis code that is matched to the channel. The second contribution of this paper are tight lower bounds for the mutual information rate (MIR) of Markov sources on ISI channels with finite input and output alphabets. The bounds can be evaluated within a small trellis window without using Monte Carlo methods.
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