The Secrecy Capacity of The Gaussian Wiretap Channel with Rate-Limited Help

TL;DR

This paper analyzes the secrecy capacity of Gaussian wiretap channels with rate-limited help at the receiver and transmitter, showing that help increases capacity by the help rate regardless of help security, with specific results for various channel configurations.

Contribution

It characterizes the secrecy capacity with rate-limited help in different channel scenarios, revealing that help boosts capacity by the help rate and that help security does not affect this boost.

Findings

Help increases secrecy capacity by the help rate, regardless of help security.

Secrecy capacity is positive in reversely degraded channels without wiretap coding.

Non-secure help and independent help links can still provide capacity boosts.

Abstract

The Gaussian wiretap channel with rate-limited help, available at the legitimate receiver (Rx) or/and transmitter (Tx), is studied under various channel configurations (degraded, reversely degraded and non-degraded). In the case of Rx help and all channel configurations, the rate-limited help results in a secrecy capacity boost equal to the help rate irrespective of whether the help is secure or not, so that the secrecy of help does not provide any capacity increase. The secrecy capacity is positive for the reversely-degraded channel (where the no-help secrecy capacity is zero) and no wiretap coding is needed to achieve it. More noise at the legitimate receiver can sometimes result in higher secrecy capacity. The secrecy capacity with Rx help is not increased even if the helper is aware of the message being transmitted. The same secrecy capacity boost also holds if non-secure help is available to the transmitter (encoder), in addition to or instead of the same Rx help, so that, in the case of the joint Tx/Rx help, one help link can be omitted without affecting the capacity. If Rx/Tx help links are independent of each other, then the boost in the secrecy capacity is the sum of help rates and no link can be omitted without a loss in the capacity. Non-singular correlation of the receiver and eavesdropper noises does not affect the secrecy capacity and non-causal help does not bring in any capacity increase over the causal one.