The Secrecy Capacity of Gaussian Wiretap Channels with Rate-Limited Help at the Encoder

Abstract

The Gaussian wiretap channel (WTC) with rate-limited help, available at the transmitter/encoder (Tx), in addition to or instead of the same help at the legitimate receiver, is studied under various channel configurations. For the degraded or reversely-degraded WTC, rate-limited non-secure Tx help results in a secrecy capacity boost equal to the help rate irrespective of whether the help is causal or not. For the non-degraded WTC, the secrecy capacity boost is lower bounded by the help rate. A capacity-achieving signaling is two-phase time sharing, where wiretap coding without help is used in Phase 1 and help without wiretap coding is used in Phase 2. The secrecy capacity with Tx help is positive for the reversely-degraded channel (where the no-help secrecy capacity is zero) and no Phase 1 is needed to achieve it. Unlike the no-help case, more noise at the legitimate receiver can sometimes result in higher secrecy capacity with Tx help. In the case of the joint Tx/Rx non-secure help, one help link can be omitted without affecting the capacity.