The asymptotic performance of Reed-Solomon (RS)-coded M-ary orthogonal signaling with ratio-threshold test (RTT) type demodulation in a Rayleigh-fading channel is considered. We show that the minimum E~/sub b//N/sub 0/ needed for error-free communication is eln2 (2.75 dB) with RTT, and 4.79 (6.8 dB) with hard decisions. The optimum code rate that minimizes the required E~/sub b//N/sub 0/ is e/sup -1/ with RTT and 0.46 with hard decision, and the optimum ratio threshold approaches 1 for large M. Next, we investigate the fundamental limit in a direct-sequence spread-spectrum multiple-access (DS/SSMA) system employing an M-ary orthogonal code of length N=Mm, which is obtained by spreading every row of an M/spl times/M Hadamard matrix with a user-specific random sequence of length N. We derive the minimum E~/sub b//N/sub 0/ for error-free communication as a function of the number of users, the optimum code rate that minimizes E~/sub B//N/sub 0/, and the maximum limit on the total information transmission rate. Then, we consider a multirate DS/SSMA system, where a population of users simultaneously transmit at different power levels a variety of traffic types of different information rates. We derive the minimum required E~/sub B//n/sub 0/ and the optimum code rate for each traffic type.