Polar codes for the two-user multiple-access channel

TL;DR

This paper extends Arikan's polar coding to two-user multiple-access channels, demonstrating channel polarization to extremals with optimal uncoded transmission, achieving the sum rate for uniform inputs with efficient encoding, decoding, and low error probability.

Contribution

It introduces a polar coding scheme for two-user MACs that achieves optimal sum rate and maintains low complexity similar to single-user polar codes.

Findings

Channels polarize to five extremals with optimal uncoded transmission.

Achieves sum rate corresponding to uniform input distributions.

Encoding and decoding complexity remains $O(n\log n)$ with low error probability.

Abstract

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 correponds 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 $o(\exp(-n^{1/2-\epsilon}))$ for block error probability, where $n$ is the block length.