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This paper presents detailed results on the relative merits of encoding blocks of binary digits into a set of equiprobable, equal energy, orthogonal signals each containing n bits of information. During a time interval of T seconds, one signal from this set is selected and transmitted over the ``Rician'' channel, further perturbed by additive white Gaussian noise and noncoherently detected at the receiver by matched filters and follow-up envelope detectors. Word and bit error probabilities (and bounds on these) are graphically illustrated for various degrees of coding and for various forms of the channel model. Particular emphasis is placed on the Gaussian channel. Special cases of Viterbi's results for coded phase-coherent communications are compared with those obtained in this paper. Bandwidth considerations are also discussed. The results are useful to the engineer who is faced with the problem of designing coded communication systems where power is limited to the point that phase coherence cannot be established at the receiver. Typical examples are space communications where it is desired to telemeter scientific data from small scientific satellites or space probes or for scatter-channel links which are to be used for relaying data between two widely separated points on the earth.