The Capacity-Distortion Function For Multihop Channels With State

Communication over channels with state is a classical problem extensively studied. Herein, the problem statement is extended to consider a multihop channel where the channel state information in hops, unavailable to neither the source, the destination, nor the relay(s), is to be estimated at the destination, along with reliable information transmission. Each relay in the multihop channel forwards the source's transmitted signal, estimates the preceding hops' channel states, and assists in the destination's reliable decoding of the transmitted message and reconstruction of the channel states. For a two-hop channel with independent states over the two hops, it is shown that a decode-(indirectly)-compress-and-forward strategy achieves the capacity-distortion function.