In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian multiple-input multiple-output (MIMO) broadcast channel. An eavesdropper also receives the transmitted signal via another MIMO channel. We first consider the discrete memoryless channel and obtain the capacity region of the degraded channel. The secret dirty paper coding (SDPC) region as an achievable rate region for the general discrete channel is introduced. Relying on the results for the discrete channel, we fully characterize the secrecy capacity region of MIMO broadcast channel. It is shown that the SDPC scheme is optimal. The converse part of the proof relies on the generalized Costa's entropy power inequality and a new channel enhancement strategy in which we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged.

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.

In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information at the intended receiver is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is minimizing the distortion of source reconstruction at the intended receiver. In this work, it is shown that the source-channel separation coding scheme is optimum in the sense of achieving the minimum distortion. A hybrid digital-analog Wyner-Ziv coding scheme is then proposed which achieve the minimum distortion. This secure joint source channel coding scheme is based on Wyner-Ziv coding scheme and wiretap channel coding scheme when the analog source is not explicitly quantized. The proposed secure hybrid digital-analog scheme is analyzed under the main channel SNR mismatch. It is proven that the proposed scheme can give a graceful degradation of distortion with SNR under SNR mismatch, i.e., when the actual SNR is larger than the designed SNR.

A new achievability rate region for the secure discrete memoryless Multiple-Access-Channel (MAC) is presented. Thereafter, a novel secure coding scheme is proposed to achieve a positive Secure Degrees-of-Freedom (S-DoF) in the single-antenna MAC. This scheme converts the single-antenna system into a multiple-dimension system with fractional dimensions. The achievability scheme is based on the alignment of signals into a small sub-space at the eavesdropper, and the simultaneous separation of the signals at the intended receiver. Tools from the field of Diophantine Approximation in number theory are used to analyze the probability of error in the coding scheme.

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. It is assumed that the channels are degraded and the wire-tapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. It is shown that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged.