Analyses are presented on a variety of topics related to the transmission of digital data. The performance of several types of Phase Shift Keyed (PSK) systems, as determined by the relationship of the error probability to signal-to-noise ratio, is examined. Coherent, differentially coherent, binary and m-state PSK systems, and the effects of frequency offset, cross-talk and thermal noise on the performance of these systems are considered. The performance of m-state differentially coherent multiplexed PSK data links operating over a Rayleigh fading tropospheric scatter link is analyzed. The properties of impulse noise are examined and the effect of impulse noise on digital systems using close packed codes are investigated. Moment detection, which refers to a decision technique based on the use of temporal moments is investigated both analytically and experimentally.