Design of polar codes for broadcast channels

Abstract

Polar code, invented by Arikan, has been a hot topic in coding theory due to its elegant structure and appealing decoding complexity. Furthermore, due to its underlying polarization theory, polar codes achieved huge breakthrough on extensions of multi-user information-theoretic models, including multiple access channel, broadcast channel, and relay channel. However, proposed schemes have limitations for practical applications, due to complexity and lack of applicable scenarios.

To overcome such limitations, we focus on a simpler scheme and figure out conditions of the broadcast channel where the scheme can be applied. We formulate such problems via polarization alignment, which provides strict inequality of Bhattacharyya parameters between constructed polarization sets. We extend the applicable channels for the schemes by formulating new sufficient conditions for polarization alignment.

Finally, we propose some applications of our research. First, we show an example of broadcast channel where the alignment holds, which was previously unknown. Moreover, we compare the achievable regions between the broadcast channel polar codes and time sharing via point-to-point channel polar codes. Simulation results show the former performs better than the latter.