The Secrecy Capacity of the Wiretap Channel With Additive Noise and Rate-Limited Help

The wiretap channel with additive (possibly non-Gaussian) noise and 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) and power/amplitude constraints. For all channel configurations, the rate-limited Rx help results in a (weak or strong) secrecy capacity boost equal to the help rate. This holds irrespective of whether the help is secure or not, or whether the helper is aware of the message being transmitted or not; the secrecy of help or helper’s knowledge of the message does not provide any extra capacity boost. 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 under weak secrecy. The same 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, the capacity boost is the sum of help rates and no link can be omitted without 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. The choice of the secrecy criterion (weak/strong) affects the complexity of implementation but not the secrecy capacity. Stronger noise at the legitimate receiver can sometimes result in higher secrecy capacity.