Computable Upper Bounds on the Capacity of Finite-State Channels
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The capacity of finite-state channels (FSCs) without feedback is investigated. We derive upper bounds that depend on the choice of a test distribution on the channel output process. We show that if the test distributions are structured on directed graphs, then the upper bounds are computable for two classes of FSCs. The computability of the upper bounds, subject to such test distributions, is shown via a novel dynamic programming (DP) formulation. We evaluate our bounds for several examples, including the well-known Trapdoor and Ising channels. For these channels, our bounds are analytic, simple, and strictly better than all previously reported bounds in the literature. Moreover, by studying the dicode erasure channel (DEC) we show that extending the standard Markovian test distribution to the choice of graph-based test distributions improves significantly the performance of the upper bounds. Finally, an alternative converse for the Previous Output is STate (POST) channel is shown.
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