  We propose a communication model, that we call compound arbitrarily varying
channels (CAVC), which unifies and generalizes compound channels and
arbitrarily varying channels (AVC). A CAVC can be viewed as a noisy channel
with a fixed, but unknown, compound-state and an AVC-state which may vary with
every channel use. The AVC-state is controlled by an adversary who is aware of
the compound-state. We study three problems in this setting: 'communication',
'communication and compound-state identification', and 'communication or
compound-state identification'. For these problems, we study conditions for
feasibility and capacity under deterministic coding and random coding.
