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Characterization of super-additivity and discontinuity behavior of the capacity of arbitrarily varying channels under list decoding

The arbitrarily varying channel (AVC) models communication over a channel that varies in an arbitrary and unknown manner from channel use to channel use. This paper considers the AVC under list decoding and studies the corresponding list capacity. In particular, the list capacity function is shown to be discontinuous and the corresponding discontinuity points are characterized for all possible list sizes. For orthogonal AVCs it is then shown that the list capacity is super-additive, implying that joint encoding and decoding for two orthogonal AVCs can yield a larger list capacity than independent processing of both channels. This discrepancy is shown to be arbitrary large.