Minimum Cost Decision-Feedback Systems for Detecting Signals Perturbed by Additive Gaussian Noise

This paper is concerned with achieving reliable communications at minimum cost. It studies a means of accomplishing this in the form of a decision-feedback system. In this system binary signals are transmitted and three decisions are permitted at the receiver (1) the decision to record the presence of a signal, (2) the decision to record the absence of a signal, and (3) the decision to withhold recording a statement about the signal. Because of noise, the first decision may result in a false alarm and the second in a miss. By withholding judgment in doubtful cases, the risk of a wrong decision may be reduced providing two conditions are met (1) natural (i.e., language) or artificial (i.e., coding) constraints can be utilized within the message to interpret doubtful observations and/or (2) the transmitter can be required to repeat the signal corresponding to the doubtful observation. The latter is the method of decision feedback. The objectives of this paper are two-fold (1) to develop a theory of decision-feedback systems by means of which the optimum conditions of operation in the least cost sense can be specified and (2) to demonstrate that the method of artificial constraints for interpreting doubtful observations is less efficient in its use of the fundamental communication cost parameters, power, bandwidth, and time than decision feedback.