Randomness and dependencies extraction via polarization, with applications to Slepian-Wolf coding and secrecy

TL;DR

This paper extends polarization techniques to multiple correlated sources, enabling extraction of randomness, conversion of dependencies, and the development of efficient coding schemes for Slepian-Wolf and secret key generation.

Contribution

It introduces a polarization-based framework for multiple sources, achieving optimal secret key and compression schemes with low complexity.

Findings

Achieves secret key capacity with polarization-based schemes

Attains Slepian-Wolf capacity region efficiently

Transforms source dependencies to extremal dependencies

Abstract

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 takes the original arbitrary dependencies to extremal dependencies. Polar coding schemes for the Slepian-Wolf problem and for secret key generations are then proposed based on this phenomenon. In particular, constructions of secret keys achieving the secrecy capacity and compression schemes achieving the Slepian-Wolf capacity region are obtained with a complexity of $O(n \log (n))$.