On the capacity of a channel with action-dependent state and reversible input

We consider a problem of coding for channels with action-dependent states available noncausally to the encoder where the decoder is additionally required to be able to decode the channel input reliably. Lower and upper bounds on the channel capacity are derived. It is shown that the capacity is determined if there exists a maximizing joint probability distribution in the upper bound which satisfies the two-stage coding condition, and it, in turn, reveals the formula duality between this problem and that of source coding with common reconstruction and action-dependent side information. We also state two simple coding schemes and the corresponding achievable rates for the cases where the two-stage coding condition is not fulfilled.