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In this work, we study two models of arbitrarily varying channels, whencausal side information is available at the encoder in a causal manner. First,we study the arbitrarily varying channel (AVC) with input and stateconstraints, when the encoder has state information in a causal manner. Lowerand upper bounds on the random code capacity are developed. A lower bound onthe deterministic code capacity is established in the case of amessage-averaged input constraint. In the setting where a state constraint isimposed on the jammer, while the user is under no constraints, the random codebounds coincide, and the random code capacity is determined. Furthermore, forthis scenario, a generalized non-symmetrizability condition is stated, underwhich the deterministic code capacity coincides with the random code capacity.  A second model considered in our work is the arbitrarily varying degradedbroadcast channel with causal side information at the encoder (withoutconstraints). We establish inner and outer bounds on both the random codecapacity region and the deterministic code capacity region. The capacity regionis then determined for a class of channels satisfying a condition on the mutualinformations between the strategy variables and the channel outputs. As anexample, we show that the condition holds for the arbitrarily varying binarysymmetric broadcast channel, and we find the corresponding capacity region.

A Study on Arbitrarily Varying Channels with Causal Side Information at the Encoder