(SNR). In the case of realistic duty cycle constraint, numerical results also show that the rate achieved by the Markov process is substantially higher than that achieved by any i.i.d. input. This suggests that, compared to intermittently transmitting packets using Gaussian or Gaussian-like signaling, it is more efficient to disperse nontransmission symbols within each packet to form codewords, which results in a form of on-off signaling. One of the reasons for the superiority of on-off signaling is that the positions of nontransmission symbols can be used to convey information, the impact of which is particularly significant in case of low SNR or low duty cycle. This has been observed in the past. For example, as shown in [11] (see also [12], [13]), time sharing or time-division duplex (TDD) can fall considerably short of the theoretical limits in a relay network: The capacity of a cascade of two noiseless binary bit pipes through a half-duplex relay is 1.14 bits per channel use, which far exceeds the 0.5 bit achieved by TDD and even the 1 bit upper bound on the rate of binary signaling. Besides that duty cycle constraint is frequently seen in practice, another motivation of this study is a recent work [14], in which on-off signaling is proposed for a clean-slate design of wireless ad hoc networks formed by half-duplex radios. Using this signaling scheme, which is called rapid on-off-division duplex (RODD), a node listens to the channel and receives useful signals during its own off symbols within each frame. Each node can transmit and receive messages at the same time over one frame interval, thereby achieving (virtual) full-duplex communication. Understanding the impact of duty cycle constraint is crucial to characterizing the fundamental limits of such wireless networks. Consider digital communication systems where coded data are mapped to waveforms for transmission. Usually there is a collection of pulse waveforms, where each pulse represents a symbol (or letter) from a discrete alphabet. We view nontransmission over a symbol interval as transmitting the all zero waveform. In other words, a symbol interval of nontransmission is simply regarded as transmitting a special symbol “0,” which carries no energy. As far as the capacity-achieving input is concerned it suffices to consider the baseband discrete-time 4 II. SYSTEM MODEL