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A discrete compound channel with memory is considered, where no stationarity,ergodicity or information stability is required, and where the uncertainty setcan be arbitrary. When the discrete noise is additive but otherwise arbitraryand there is no cost constraint on the input, it is shown that the causalfeedback does not increase the capacity. This extends the earlier resultobtained for general single-state channels with full transmitter (Tx) channelstate information (CSI) to the compound setting. It is further shown that, forthis compound setting and under a mild technical condition on the additivenoise, 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 canalso be expressed as a saddle-point in the information-theoretic game betweenthe transmitter (who selects the input distribution) and the nature (whoselects the channel state), even though the objective function (theinf-information rate) is not convex/concave in the right way. Cases where theTx CSI does increase the capacity are identified.  Conditions under which the strong converse holds for this channel arestudied. The ergodic behaviour of the worst-case noise in otherwiseinformation-unstable channel is shown to be both sufficient and necessary forthe strong converse to hold, including feedback and no feedback cases.

Feedback Does Not Increase the Capacity of Compound Channels with Additive Noise