Randomness and Dependencies Extraction via Polarization, With Applications to Slepian-Wolf Coding and Secrecy
The polarization phenomenon for a single source is extended to a framework with multiple correlated sources. It is shown in addition to extracting the randomness of the source, the polar transforms take the original arbitrary dependencies to extremal dependencies. Polar coding schemes for the Slepian-Wolf (SW) coding problem and for secret key generations are then proposed based on this phenomenon. In particular, secret keys achieving the secrecy capacity and compression schemes achieving the SW capacity region are obtained with a complexity of O(n log(n)).