Recently, there has been a lot of research on multi-user superposition coding under the umbrella of 
non-orthogonal multiple  access (NOMA). In almost all cases, a perfect knowledge of the distributed channel state information (CSI) is assumed. 
In this work, we study the effects of limited feedback on NOMA. Instead of perfect CSI, we assume 
each receiver only has access to its own local CSI, from the BS to itself, and broadcasts its feedback 
information using a limited number of bits.
We prove that the losses in the minimum rate and outage probability, compared with the perfect CSI, decay at least exponentially with the feedback rate. 
We also design simple but efficient quantizers for NOMA.