Optimal communication systems with noiseless feedback for a binary source and white Gaussian channel

The sequential and nonsequential feedback systems for a binary source, first proposed by Turin, are considered. It is shown that in both cases the optimal signals belong to the family , where is arbitrary. In the sequential scheme the bound on transmission rate is achieved for any by all members of this family, and in the nonsequential scheme for small only. The optimal signals within this family, i.e., signals for which peak power/average power is minimal, result if . In the sequential case, the optimal scheme is compared with two suboptimal schemes, and the advantages of the first are demonstrated. Finally, the problem of sequential detection with time-varying thresholds is presented, and its equivalence to a problem with fixed thresholds is proved.