Large on the capacity of indecomposable finite-state channels with feedback

We study the capacity of indecomposable finite-state channels (FSCs) with feedback. In this class of channels, the effect of the initial state on the state transition probabilities for every given input sequence becomes negligible as time evolves. It is known that for indecomposable FSCs without feedback the capacity is independent of the initial state. Similar results were obtained for indecomposable finite-state multiple access channels and indecomposable degraded finite-state broadcast channels. However, when feedback is present, such a result does not exist except for FSCs without intersymbol interference (ISI). In this paper we show that the capacity-achieving distribution of indecomposable FSCs with feedback can be computed without minimizing over all initial channel states.