Effect of feedback on the capacity of discrete additive channels with memory

We consider discrete channels with arbitrary additive noise. Note that such channels need not be memoryless; in general, they have memory. We show that feedback does not increase the capacity of such channels. The same result is also shown for a larger class of channels to which additive channels belong, the class of discrete symmetric channels with memory. These channels have the property that their infinite-information rate is maximized for equally likely iid input processes. Finally, we impose cost constraints on the input of the additive channels, rendering them non-symmetric. In this case, we show that feedback can increase their capacity-cost function