Polar Codes for the -User Multiple Access Channel

——In this paper, polar codes for the -user multiple access channel (MAC)with binary inputs are constructed. It is shown that Arikan’’s polarization technique applied individually to each user transforms independent uses of an -user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: 1) the ““uniform sum-rate”” of the original MAC is preserved, 2) the extremal MACs have uniform rate regions that are not only polymatroids but matroids, and thus, 3) their uniform sum-rate can be reached by each user transmitting either uncoded or xed bits; in this sense, they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of (where is the block length), a block error probability of , and capable of achieving the uniform sum-rate of any binary input MAC with arbitrary many users. Applications of this polar code construction to channels with a nite eld input alphabet and to the additive white Gaussian noise channel are also discussed. Index Terms——Matroid, multiuser communication, multiple access channel (MAC), polar codes, polarization.