  A discrete compound channel with memory is considered, where no stationarity,
ergodicity or information stability is required, and where the uncertainty set
can be arbitrary. When the discrete noise is additive but otherwise arbitrary
and there is no cost constraint on the input, it is shown that the causal
feedback does not increase the capacity. This extends the earlier result
obtained for general single-state channels with full transmitter (Tx) channel
state information (CSI) to the compound setting. It is further shown that, for
this compound setting and under a mild technical condition on the additive
noise, the addition of the full Tx CSI does not increase the capacity either,
so that the worst-case and compound channel capacities are the same. This can
also be expressed as a saddle-point in the information-theoretic game between
the transmitter (who selects the input distribution) and the nature (who
selects the channel state), even though the objective function (the
inf-information rate) is not convex/concave in the right way. Cases where the
Tx CSI does increase the capacity are identified.
  Conditions under which the strong converse holds for this channel are
studied. The ergodic behaviour of the worst-case noise in otherwise
information-unstable channel is shown to be both sufficient and necessary for
the strong converse to hold, including feedback and no feedback cases.
