  The problem of state communication over a discrete memoryless channel with
discrete memoryless state is studied when the state information is available
strictly causally at the encoder. It is shown that block Markov encoding, in
which the encoder communicates a description of the state sequence in the
previous block by incorporating side information about the state sequence at
the decoder, yields the minimum state estimation error. When the same channel
is 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 and the state estimation error is characterized via the
capacity- distortion function. It is shown that any optimal tradeoff pair can
be achieved via rate-splitting. These coding theorems are then extended
optimally to the case of causal channel state information at the encoder using
the Shannon strategy.
