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Transmitting digital information using ultra-short pulses, impulse radio (IR) has received increasing interest for multiple access (MA). When IRMA systems have to operate in dense multipath environments, the multiple user interference (MUI) and intersymbol interference (ISI) induced, adversely affect system capacity and performance. Analog IRMA utilizes pulse position modulation (PPM) and random time-hopping codes to mitigate ISI and suppress MUI statistically. We develop an all-digital IRMA scheme that relies on multistage block-spreading (MS-BS), and judiciously designed transceiver pairs to eliminate MUI deterministically, and regardless of ISI multipath effects. Our proposed MS-BS-IRMA system can accommodate a large number of users and is capable of providing different users with variable transmission rates, which is important for multimedia applications. Unlike conventional IRMA systems, MS-BS-IRMA exhibits no degradation in bit-error rate performance, as the number of users increases.