Secure joint source–channel coding with interference known at the transmitter
In this study, the problem of transmitting an independent and identically distributed (i.i.d.) Gaussian source over an i.i.d. Gaussian wire-tap channel, with an i.i.d. Gaussian known interference available at the transmitter is considered. The intended receiver is assumed to have a certain minimum signal-to-noise ratio (SNR) and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is to minimise the distortion of source reconstruction at the intended receiver. In this study, an achievable distortion is derived when Shannon's source–channel separation coding scheme is used. Three hybrid digital–analogue secure joint source–channel coding schemes are then proposed, which achieve the same distortion. The first coding scheme is based on Costa's dirty-paper-coding scheme and wire-tap channel coding scheme, when the analogue source is not explicitly quantised. The second coding scheme is based on the superposition of the secure digital signal and the hybrid digital–analogue signal. It is shown that for the problem of communicating a Gaussian source over a Gaussian wire-tap channel with side information, there exists an infinite family of secure joint source–channel coding schemes. In the third coding scheme, the quantised signal and the analogue error signal are explicitly superimposed. It is shown that this scheme provides an infinite family of secure joint source–channel coding schemes with a variable number of binning. Finally, the proposed secure hybrid digital–analogue schemes are analysed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, that is, when the actual SNR is larger than the designed SNR.
