State-dependent channels with composite state information at the encoder

State-dependent channels have received much attention over the years, due to their relevance in many different network and multi-user communication scenarios. Nonetheless, previous treatments of this problem assumed that all of the state is available in the same manner: causally, non-causally or non-causally with a finite look-ahead. Yet, in many realistic situations, different parts of the state are known in a different manner. We consider the case where the state is composed of several parts, where each part is known with a different look-ahead. Specifically, we derive the capacity for the case where part of the state is known non-causally to the transmitter, whereas the other part is known only causally, and demonstrate that there are cases in which this capacity can be strictly larger that the capacity of the case where the state is known in a causal fashion, and strictly smaller than the capacity of the same channel, where the state is available non-causally. We note that the treatment in this work provides a unified framework for treating the causal state-information case, the non-causal state-information case, as well as a mixture of the two.