Paper detail

Non-existence of certain kind of finite-letter mutual information characterization for a class of time-invariant Markoff channels

We provide a rigorous definition of a certain kind of characterization for capacity regions of a family of Markoff networks which is based on optimization problems resulting out of calculating conditional mutual information from a finite number of random variables and by constraining these random variables in a certain way. This definition is partly motivated by the definition of single-letter characterizations in information theory. For a point-to-point Markoff channel, we prove that approximating the solution to these characterizations within an additive constant is a computable problem. Based on previous undecidability results concerning capacities of certain class of finite state machine channels (FSMCs), it will follow that there exists an example of family of FSMCs for which given such a characterization, this characterization cannot represent the capacity of this family of FSMCs.