Competitive Analysis of Arbitrary Varying Channels

Arbitrary varying channels (AVC) are used to model communication settings in which a channel state may vary arbitrarily over time. Their primary objective is to circumvent statistical assumptions on channel variation. Traditional studies on AVCs optimize rate subject to the worst-case state sequence. While this approach is resilient to channel variations, it may result in low rates for state sequences that are associated with relatively good channels. This paper addresses the analysis of AVCs through the lens of competitive analysis, where solution quality is measured with respect to the optimal solution had the state sequence been known in advance. Our main result demonstrates that codes constructed by a single input distribution do not achieve optimal competitive performance over AVCs. This stands in contrast to the single-letter capacity formulae for AVCs, and it indicates, in our setting, that even though the encoder cannot predict the subsequent channel states, it benefits from varying its input distribution as time proceeds.