Channel-aware assignment of subchannels to users in the downlink of an OFDMA system requires extensive feedback of channel state information (CSI) to the base station. Since bandwidth is scarce, schemes that limit feedback are necessary. We develop a novel, low feedback, distributed splitting-based algorithm called SplitSelect to opportunistically assign each subchannel to its most suitable user. SplitSelect explicitly handles multiple access control aspects associated with CSI feedback, and scales well with the number of users. In it, according to a scheduling criterion, each user locally maintains a scheduling metric for each subchannel. The goal is to select, for each subchannel, the user with the highest scheduling metric. At any time, each user contends for the subchannel for which it has the largest scheduling metric among the unallocated subchannels. A tractable asymptotic analysis of a system with many users is central to SplitSelect's simple design. Extensive simulation results demonstrate the speed with which subchannels and users are paired. The net data throughput, when the time overhead of selection is accounted for, is shown to be substantially better than several schemes proposed in the literature. We also show how fairness and user prioritization can be ensured by suitably defining the scheduling metric. [ABSTRACT FROM AUTHOR]