Polar codes for Slepian-Wolf, Wyner-Ziv, and Gelfand-Pinsker

Polar codes, combined with successive cancellation algorithms, are known to be asymptotically optimal for both the channel as well as the lossy source coding problem. The complexity of the encoding and the decoding algorithm in both cases is O(N log(N)), where N is the blocklength of the code. We show that polar codes also achieve optimum performance for the Slepian-Wolf, the Wyner-Ziv, and the Gelfand-Pinsker problem. The optimality of polar codes for these scenarios rests on the fact that polar codes are optimal for both the channel and the lossy source coding problems. Our results extend to general versions of these problems.