### Abstract

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 language | English (US) |
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Article number | 6208869 |

Pages (from-to) | 5437-5448 |

Number of pages | 12 |

Journal | IEEE Transactions on Information Theory |

Volume | 58 |

Issue number | 8 |

DOIs | |

State | Published - 2012 |

### All Science Journal Classification (ASJC) codes

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

### Keywords

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

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## Cite this

*IEEE Transactions on Information Theory*,

*58*(8), 5437-5448. [6208869]. https://doi.org/10.1109/TIT.2012.2201374