On Channel Sensitivity to Partially Known Two-sided State Information

In some situations of channel coding with state information (CCSI), the encoder and/or the decoder 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 consider the general case of channel with arbitrary pair of independent and identically distributed (i.i.d), possibly correlated, state information (S1, S2) available at the transmitter and at the receiver, respectively. We first analyze the decrease in capacity, or channel sensitivity to this perturbing noise. Both lower and upper bounds on this channel sensitivity are provided, using Fisher Information. The lower bound turns to be relatively tight, at low Signal-to-Noise-Ratio (SNR), in the Gaussian case, for which we provide a closed form expression of channel capacity degradation. Next, we show that these results can be used so as to increase system immunity to noise, by adapting the encoder to the channel uncertainty. Also, we straightforwardly extend these results to the more practical case where the state information is known only causally at the transmitter. Finally, for illustration purposes, two possible applications in the non-causal and the causal case, respectively, are discussed.