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We consider a binary pulsed communication system, with possibly episodic transmission, i.e., the system transmits n pulses per information bit and allows for off-time separation between pulses. In the ultra-wideband (UWB) regime, such systems are motivated for overlay applications, as well as low probability of intercept and low probability of detection scenarios. Processing gain enables low-power transmission, and the UWB pulsing limits the interference effects into narrowband systems. We introduce a random ternary sequence model and use this to study multiuser system performance. We consider the issues of processing gain, jamming margin, coding gain, and multiuser interference (MUI) for a single-user matched filter receiver. The introduction of episodic transmission, with a corresponding reduction in bit rate, provides system flexibility with respect to both MUI rejection and handling multipath channels. Highly episodic transmission provides nearly orthogonal low-rate users, even with system asynchrony and no power control. Performance of a single-user RAKE receiver is evaluated via a Chernoff bound on bit error rate, in the presence of MUI. The analysis includes the impact of fading as well as pilot-aided channel estimation.