Indecomposable finite state channels and primative approximation

The class of discrete stationary channels with memory that can be arbitrarily well approximated by indecomposable finite state channels is investigated. The concept of channel distance is used to quantify the notion of one channel approximating another, and it is shown that the class of interest equals the class of channels approximable by nonanticipating primitive channels. The latter class includes all nonanticipating finite memory channels and all nonanticipating -continuous, conditional almost block independent (CABI) channels. In addition, it is shown that for a large class of finite state channels, continuity and CABI imply indecomposability.