Computable Upper Bounds on the Capacity of Finite-State Channels

We consider the use of well-known dual capacity bounding technique for deriving upper bounds on indecomposable finite-state channels (FSCs) with finite input and output alphabets. In this technique, are obtained by choosing suitable test distributions sequence channel outputs. propose that arise from certain graphical structures called Q-graphs. As we show in paper, advantage choice distribution is that, important sub-classes unifilar input-driven FSCs, resulting can be formulated as a dynamic programming (DP) problem, which makes tractable. illustrate several examples where able to solve associated DP problems explicitly obtain either match or beat best previously reported bounds. For instance, classical trapdoor channel, improve known bound 0.661 (due Lutz (2014)) 0.584, shrinking gap lower 0.572, all being units bits per use.