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Markov Processes Asymptotically Achieve the Capacity of Finite-State Intersymbol Interference Channels

Recent progress in capacity evaluation has made it possible to compute a sequence of lower bounds on the capacity of a finite-state intersymbol-interference (ISI) channel by finding a sequence of optimized Markov input processes with increasing order , for which the state of the process is the previous input symbols. In this correspondence, we prove that, as the order goes to infinity, the sequence of optimized Markov sources asymptotically achieves the capacity of the channel. The conclusion is extended to two-dimensional finite-state ISI channels, the binary symmetric channel (BSC) with constrained inputs, and general indecomposable finite-state channels with a mild constraint.