Polar codes for the two-user binary-input multiple-access channel

Arikan´s polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of which uncoded transmission is optimal. The sum rate achieved by this coding technique is the one that corresponds to uniform input distributions. The encoding and decoding complexities and the error performance of these codes are as in the single-user case: O(n log n) for encoding and decoding, and o(exp(-n^½-∈)) for block error probability, where n is the block length.