A multi-rate interleaved frequency division multiple access (IFDMA) modulation scheme permits users to transmit at different data rates or to vary their data rates while providing frequency diversity and preserving low peak-to-average power ratios and orthogonality between user data rates. The modulation scheme allows user-specific data block and repetition sizes, as well as user-specific modulation codes. Code assignment rules are provided for maintaining orthogonality between the different user data rates. Block and phase ramp modulation codes can be used. Asynchronous transmissions by users are supported by ensuring that the length of the cyclic extension is sufficiently long to tolerate worst case relative signal arrival delays between users and the channel pulse response duration over the communication medium. The modulation scheme can be employed in wireless communication systems, such as cellular or paging systems.