Optimal quantization for finite-state channels

Optimal scalar quantizer design for transmission over a finite-state channel is considered. The objective is to minimize the mean-squared error when the channel is in the normal mode of operation, while guaranteeing a minimum fidelity when the channel is in the ''bad'' state. An optimal quantizer design algorithm for the general case where noisy state information is available both at the receiver and at the transmitter is derived. It is shown that using mixed strategies is necessary in order to achieve the optimal performance. Finally, the case where the observation is noisy is considered and it is shown that the optimal scheme in this case is to apply the algorithm for the ''no observation noise'' to the mean-squared estimate of the desired random variable from the noisy data.