Universal polar codes for more capable and less noisy channels and sources

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,Z there 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,Y when using successive cancellation decoding, at least when the channel PY|X is more capable than PZ|X and PX is such that it maximizes I(X; Y )-I(X;Z) for the given channels PY|X and 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.

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