Studies of sequential detection systems with uncertainty feedback

The problem studied is the design of signals in a binary sequential detection system which has a feedback channel available to it. Until a decision is made on a particular transmission, the transmitter is informed via the feedback channel of the state of uncertainty at the receiver. This uncertainty feedback modulates the transmitted signal so that, for a prescribed probability of error, the average time of transmission of a binary digit is minimized subject to an average power constraint and a probabilistic peak power constraint. It is assumed that the forward and the feedback channels are coherent and are each disturbed independently by white Gaussian noise. Previous work has been predicated on noise-free feedback. Signals are derived, drawn from a certain class, which are optimum when the ratio of allowable peak-to-average power is either large or close to one. The performance of these signals is analyzed. It is shown that for a high signal-to-noise ratio in the feedback channel and a high allowable peak-to-average power ratio one can transmit at approximately channel capacity with Iow probability of error. However, an infinite feedback channel signal-to-noise ratio and an infinite allowable peak-to-average power ratio are required to transmit at channel capacity with zero probability of error. Results on signal design in a system whose configuration is slightly different from that considered in the main body of the paper are summarized, as well as the results of a study of the effect of delay in the forward and feedback channels.