On channels with asynchronous state information at the transmitter

A state dependent channel with asynchronous side information at the transmitter is introduced. It is assumed that the state information sequence is a possibly delayed version of the state sequence. The encoder and the decoder are aware of the fact that the state information might be delayed, and an upper bound on the delay is also known, but other than that, they are ignorant of the actual delay. We consider both the causal and the non-causal cases and present achievable rates for these channels, and the corresponding coding schemes. In the non-causal case, the coding scheme is based on an adaptation of the Gelfand-Pinsker binning scheme. In the causal case, we present a coding scheme whose structure depends on the values the delay may take. We further study the special case of the binary symmetric asynchronous state dependent channel with non-causal side information at the transmitter. Additionally, we find the capacity of the asynchronous Gelfand-Pinsker channel with feedback.