Upper bounds on the capacities of non-controllable finite-state channels using dynamic programming methods

A non-controllable finite-state channel (FSC) is a finite-state channel in which the user can´t control channel states. That is, the channel state of a non-controllable FSC evolves freely according to an uncontrollable probability law. Thus far, good upper bounds on capacities of general non-controllable FSCs remain unknown. Here we develop upper bounds that use delayed feedback and delayed state information, and propose dynamic programming methods to numerically evaluate the bounds.