A class of decentralized sequential detection problems is investigated. Under appropriate independence assumptions, it is shown that at each time instant the optimal local strategies are given by threshold tests on the likelihood of ratios. Furthermore, local decisions depend not only on the present and past observations, but on the past local decision as well. That is, for each local processor a different threshold exists for every different sequence of past decisions. Examples, computational techniques, discussions of the difficulties at hand, and suggestions for further exploration of the problem are presented.>

The cutoff rate is derived for a digital communication system employing an optical carrier and direct detection. The coordinated design of the encoder, optical modulator, and demodulator is then studied using the cutoff rate as a performance measure rather than the more commonly employed error probability. Modulator design is studied when transmitted optical signals are subject simultaneously to average-energy and peak-value constraints. Pulse-position modulation is shown to maximize the cutoff rate when the average-energy constraint predominates, and the best signals when the peak-value constraint predominates are identified in terms of Hadamard matrices. A time-sharing of these signals maximizes the cutoff rate when neither constraint dominates the other. Problems of efficient energy utilization, choice of input and output alphabet dimension, and the effect of random detector gain are addressed.

Lower bounds are given on the attainable mean-square performance in causally tracking the phase and frequency of a subcarrier that modulates an optical carrier in a direct-detection opticalcommunication system.