Polar Coding Without Alphabet Extension for Asymmetric Models

Junya Honda, Hirosuke Yamamoto

IEEE Transactions on Information Theory, Vol. 59, No.12, pp.7829-7838, December 2013

This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distor- tion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewords are not always uniform. It is known that such nonuniform distributions can be realized by Gallager’s scheme which maps multiple auxil- iary symbols distributed uniformly to an actual symbol. However, the complexity of Gallager’s scheme increases considerably for the case that the optimal distribution cannot be approximated by simple rational numbers. To overcome this problem for the asym- metric settings, a new polar coding scheme is proposed, which can attain the channel capacity without any alphabet extension by invoking results on polar coding for lossless compression. It is also shown that the proposed scheme achieves a better tradeoff between complexity and decoding error probability in many cases.

Index Terms : Asymmetric channels, channel coding, lossy source coding, polar codes.

Final submission version (PDF) (305Kbytes)
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

DOI: 10.1109/TIT.2013.2282305