An analysis of the timed Z-channel

Golomb analyzed the Z-channel, a memoryless channel with two input symbols and two output symbols, where one of the input symbols is transmitted with noise while the other is transmitted without noise, and the output symbol transmission times are equal. We generalize to the timed Z-channel, where the output symbol transmission times are not equal. The timed Z-channel appears as the basis for a large class of covert (communication) channels appearing in multilevel secure computer systems. We give a detailed mathematical analysis of the timed Z-channel and report a result expressing the capacity of the timed Z-channel as the log of the root of a characteristic equation. This generalizes Shannon's work on noiseless channels for this special case. We also report a new result bounding the timed Z-channel's capacity from below. We show how an interesting observation that Golomb reported for the Z-channel also holds for the timed Z-channel.