Polar codes for the m-user multiple access channel

Emmanuel Abbe, Emre Telatar

Research output: Contribution to journalArticlepeer-review

91 Scopus citations


In this paper, polar codes for the m-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 m-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 fixed bits; in this sense, they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of O(n \log n) (where n is the block length), a block error probability of o(\exp (- n 1/2 - varepsilon), 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 finite field input alphabet and to the additive white Gaussian noise channel are also discussed.

Original languageEnglish (US)
Article number6208869
Pages (from-to)5437-5448
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Matroid
  • multiple access channel (MAC)
  • multiuser communication
  • polar codes
  • polarization


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