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.

翻译：任意变化信道（AVC）用于建模信道状态随时间任意变化的通信场景，其主要目的是规避对信道变化的统计假设。传统AVC研究针对最坏状态序列优化传输速率，虽然这种方法对信道变化具有鲁棒性，但对于对应相对较好信道的状态序列可能导致低速率。本文通过竞争性分析的视角研究AVC，其中解决方案的质量以预先知晓状态序列时的最优解为基准进行衡量。我们的主要结果表明，由单一输入分布构建的编码无法在AVC上实现最优竞争性能。这与AVC的单字母容量公式形成鲜明对比，表明在我们的设定中，即使编码器无法预测后续信道状态，随时间调整输入分布仍能带来性能增益。