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One of the features characterizing almost every multiple-access (MA) communication system is the processing gain. Through the use of spreading sequences, the processing gain of random code-division multiple-access (RCDMA) systems, or any other code-division multiple-access (CDMA) systems, is devoted to both bandwidth expansion and orthogonalization of the signals transmitted by different users. Another type of MA system is impulse radio (IR). IR systems promise to deliver high data rates over ultra-wideband channels with low-complexity transmitters and receivers. In many aspects, IR systems are similar to time-division MA systems, and the processing gain of IR systems represents the ratio between the actual transmission time and the total time between two consecutive transmissions (on-plus-off-to-on ratio). While CDMA systems, which constantly excite the channel, rely on spreading sequences to orthogonalize the signals transmitted by different users, IR systems transmit a series of short pulses, and the orthogonalization between the signals transmitted by different users is achieved by the fact that most of the pulses do not collide with each other at the receiver. In this paper, a general class of MA communication systems that use both types of processing gain is presented, and both IR and RCDMA systems are demonstrated to be two special cases of this more general class of systems. The bit-error rate of several receivers as a function of the ratio between the two types of processing gain is analyzed and compared, under the constraint that the total processing gain of the system is large and fixed. It is demonstrated that in non-intersymbol interference (ISI) channels, there is no tradeoff between the two types of processing gain. However, in ISI channels, a tradeoff between the two types of processing gain exists. In addition, the suboptimality of RCDMA systems in frequency-selective channels is established.