Universal polar codes for more capable and less noisy channels and sources
David F. Sutter, Joseph M. Renes · 2014
We prove two results on the universality of polar codes for source coding and channel communication. First, we show that for any polar code built for a source PX,Zthere exists a slightly modified polar code-having the same rate, the same encoding and decoding complexity and the same error rate-that is universal for every source PX,Ywhen using successive cancellation decoding, at least when the channel PY|Xis more capable than PZ|Xand PXis such that it maximizes I(X; Y )-I(X;Z) for the given channels PY|Xand PZ|X. This result extends to channel coding for discrete memoryless channels. Second, we prove that polar codes using successive cancellation decoding are universal for less noisy discrete memoryless channels.