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In the customary methods of transmitting binary data the receiver, as a result of the decision process made on each transmitted pulse, prints out one of two symbols. Schemes are considered here in which the receiver prints out one of three symbols (single-null zone reception) or one of four symbols (double-null zone reception). These extra symbols permit the receiver to indicate when the a posteriori probabilities of the two transmitted states are nearly equal. Single-null zone reception is shown to be capable, under optimum conditions, of achieving about one-half of the improvement in information rate theoretically attainable by increasing the number of receiver levels without limit. Double-null reception, which splits the null zone and thereby retains polarity information, offers only a slight additional increase in rate. It affords a significant advantage over single-null reception, though, because it is much less sensitive to variations in null level.