The capacity of unifilar finite-state channels with feedback has been recently derived in the form of a single-letter expression and it has been evaluated analytically for a number of channels of interest, such as the trapdoor channel and the Ising channel with feedback. In this paper, we investigate transmission schemes for this class of channels. These schemes are inspired by the posterior matching scheme (PMS) introduced for memoryless channels with feedback. The transmission scheme is proven to achieve zero rate and is conjectured to achieve channel capacity.
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