Capacity-distortion trade-off in channels with state

A problem of state information transmission over a state-dependent discrete memoryless channel (DMC) with independent and identically distributed (i.i.d.) states, known strictly causally at the transmitter is investigated. It is shown that block-Markov encoding coupled with channel state estimation conditioned on treating the decoded message and received channel output as side information at the decoder yields the minimum state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. The optimal tradeoff between the rate of the independent information that can be reliably transmitted and the state estimation error is characterized via the capacity-distortion function. It is shown that any optimal tradeoff pair can be achieved via a simple rate-splitting technique, whereby the transmitter appropriately allocates its rate between pure information transmission and state estimation.