Polar coding: a brief tour

Arikan's 'polar coding' is a technique to achieve the symmetric capacity of binary input memoryless channels. In this talk I will attempt to describe this technique, and briefly discuss its extensions to q-ary input channels, multiple access channels and rate-distortion coding. The underlying principle of polar coding allows one to view randomness from a different vantage. I will try to illustrate this with a recent result of Sasoglu: when a binary ergodic process is transformed by Arikan's 'polar transform' the resulting process, in the limit, consists only of fair coin flips or constants.