Abstract
Two types of feedback systems for a command channel are described. a) Complex Feedback-where, for each command, an identification is relayed back over the feedback channel. b) Decision Feedback-where the feedback channel is used only to state whether the satellite recognized the transmission as a command word. For a), the decision as to whether a command was properly received at the satellite is made on the ground, while for b), the decision is made at the satellite, the only purpose of the feedback channel being to cause the ground station to retransmit the command word if the satellite did not recognize the initial transmission. The decision feedback system then amounts to a one-way channel, since the satellite makes a decision after the initial transmission as to whether or not a command word was sent. If the transmitted command word is interpreted as a command, whether correct or not, the ground station has no further control. The following theorem is proved rigorously: ''It is always possible to specify a decision feedback system which gives the same error performance as a given complex feedback system.''
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