On Coding With a Partial Knowledge of the State Information

In some situations of channel coding with state information (CCSI) available at the transmitter, the encoder may not have perfect knowledge of the state information. In these situations, the state information may be viewed as the sum of a dominant (nominal) state information and a relatively weak perturbation. We analyze the decrease in capacity, or sensitivity of channel capacity to this perturbing noise. We first address the decrease in Gelfand-Pinsker capacity due to the situation and use Fisher information to give both lower and upper bounds on channel sensitivity. These bounds translate to upper and lower bounds on channel capacity, respectively. We also provide closed form expression of channel sensitivity in the Gaussian case and discuss the practical usefulness of the above bounds. For instance, we show that under certain conditions, the encoder should adapt to the available knowledge of the channel by changing its encoding strategy. Next, we show that these results can be straightforwardly extended to the general vector channel case and to the case when the state information is known only causally. Finally, for illustration purposes we give two possible applications in the non-causal and the causal case, respectively