Whereas a number of practical coding constructions (e.g. Turbo codes and Low Density 
Parity Check codes) can empirically approach the capacity of single-user communication 
channels, there is still an absence of good practical coding schemes for multi-user 
communication channels.  In this talk, we extend the polar coding method to two-user 
multiple-access communication channels. We have shown that if the two users use the 
channel combining and splitting construction, the resulting multiple-access channels will 
polarize to one of five possible extremals, on each of which uncoded transmission is 
optimal.  Our coding technique can achieve some of the optimal transmission rate pairs 
obtained with uniformly distributed inputs.  The encoding and decoding complexity of 
the code is O(n log n) with n being the block length, and the block error probability is 
roughly O(2^{-\sqrt{n}}).