EE Special Seminar

A general formula for the capacity of arbitrary compound channels, which are not necessarily

ergodic, stationary or information-stable and where the channel state set is arbitrary, is obtained using the information density approach. A direct (constructive) proof is given. To prove achievability, we generalize Feinstein Lemma to the compound channel setting, and to prove converse, we generalize Verdu-Han Lemma to the same compound setting. This extends the general formula for channel capacity of Verdu and Han  to arbitrary compound channels (not necessarily finite-state or countable). When compound channel is uniform, the general formula reduces to the familiar sup−inf expression. The compound inf-information rate plays a prominent role in the  general formula. Its properties are studied and a link between information-unstable and information-stable regimes of a compound channel is established, resulting in sufficient and necessary conditions for the strong converse to hold. The results are extended to include epsilon-capacity of compound channels. Some flaws in the known results are pointed out.