The main focus of space-time coding design and analysis for MIMO systems has been so far focused on single-user systems. For single-user systems, transmit diversity schemes suffer a loss in spectral efficiency if the receiver is equipped with more than one antenna, making them unsuitable for high rate transmission. One such transmit diversity scheme is the cyclic delay diversity code (CDD). The advantage of CDD over other diversity schemes such as orthogonal space-time block codes (OSTBC) is that a code rate of one and delay optimality are achieved independent of the number of transmit antennas. In this work we analyze the ergodic rate of a multi-user multiple access channel (MAC) with each user applying such a cyclic delay diversity (CDD) code. We derive closed form expressions for the ergodic sum-rate of multi-user CDD and compare it with the sum-capacity. We study the ergodic rate region and show that in contrast to what is conventionally known regarding the single-user case, transmit diversity schemes are viable candidates for high rate transmission in multi-user systems. Finally, our theoretical findings are illustrated by numerical simulation results.