Key Capacity with Limited One-Way Communication for Product Sources

TL;DR

This paper demonstrates that rate splitting is optimal for secret key agreement with limited one-way communication for product sources, providing new insights into the data processing inequality and deriving a water-filling solution for Gaussian sources.

Contribution

It introduces the optimality of rate splitting for secret key agreement in product sources and derives a water-filling solution for Gaussian sources with eavesdroppers.

Findings

Rate splitting is optimal for secret key agreement with limited one-way communication.

Provides an alternative proof of the tensorization property of a strong data processing inequality.

Derives a water-filling solution for Gaussian sources with eavesdroppers.

Abstract

We show that for product sources, rate splitting is optimal for secret key agreement using limited one-way communication at two terminals. This yields an alternative proof of the tensorization property of a strong data processing inequality originally studied by Erkip and Cover and amended recently by Anantharam et al. We derive a `water-filling' solution of the communication-rate--key-rate tradeoff for two arbitrarily correlated vector Gaussian sources, for the case with an eavesdropper, and for stationary Gaussian processes.