In this paper, we consider the time-slotted ALOHA packetized multiple-access system where the transmission channels obey i.i.d (independent identically distributed) Rayleigh fading. Two fundamental problems are considered. The first one is the calculation of system capacity, and the second one is how to select a channel coding for the system achieving its capacity. Here we firstly review the single time slotted capacity, and present the total capacity expression with the knowledge of channel side information. Then we deduce a threshold θ for transmission probability in a single time slot provided that all the users have the same transmission probability. It will be proved that when transmission probability is greater than the threshold θ, low-resolution code can help the system achieve its capacity. Moreover, we present an explicit threshold estimation, and prove that it can be extended to a more general case when transmission probabilities are approximately equal. In the end, simulation and numerical results show the validity and robustness of theoretical results.