7 research outputs found
A Counterexample to the Vector Generalization of Costa's EPI, and Partial Resolution
We give a counterexample to the vector generalization of Costa's entropy
power inequality (EPI) due to Liu, Liu, Poor and Shamai. In particular, the
claimed inequality can fail if the matix-valued parameter in the convex
combination does not commute with the covariance of the additive Gaussian
noise. Conversely, the inequality holds if these two matrices commute.Comment: 3 page
Optimum Relay Scheme in a Secure Two-Hop Amplify and Forward Cooperative Communication System
A MIMO secure two-hop wireless communication system is considered in this
paper. In this model, there are no direct links between the source-destination
and the source-eavesdropper. The problem is maximizing the secrecy capacity of
the system over all possible amplify and forward (AF) relay strategies, such
that the power consumption at the source node and the relay node is limited.
When all the nodes are equipped with single antenna, this non-convex
optimization problem is fully characterized. When all the nodes (except the
intended receiver) are equipped with multiple antennas, the optimization
problem is characterized based on the generalized eigenvalues-eigenvectors of
the channel gain matrices
The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel
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. First we 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. We
show that we only need to enhance the channels of the legitimate receivers, and
the channel of the eavesdropper remains unchanged. Then we extend the result of
the degraded case to non-degraded case. We show that the secret superposition
of Gaussian codes along with successive decoding cannot work when the channels
are not degraded. we develop a Secret Dirty Paper Coding (SDPC) scheme and show
that SDPC is optimal for this channel. Finally, we investigate practical
characterizations for the specific scenario in which the transmitter and the
eavesdropper have multiple antennas, while both intended receivers have a
single antenna. We characterize the secrecy capacity region in terms of
generalized eigenvalues of the receivers channel and the eavesdropper channel.
We refer to this configuration as the MISOME case. In high SNR we show that the
capacity region is a convex closure of two rectangular regions.Comment: 23 pages, 2 figure
Secure Hybrid Digital-Analog Coding With Side Information at the Receiver
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
available 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 to
minimize 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 minimum distortion. Two hybrid digital-analog
Wyner-Ziv coding schemes are then proposed which achieve the minimum
distortion. These secure joint source-channel coding schemes are based on the
Wyner-Ziv coding scheme and wiretap channel coding scheme when the analog
source is not explicitly quantized. The proposed secure hybrid digital-analog
schemes are analyzed 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, i.e., when the actual SNR is larger than the designed SNR
Secure Joint Source-Channel Coding With Side Information
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 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 unlike
the Gaussian wiretap channel without side information, Shannon's source-channel
separation coding scheme is not optimum in the sense of achieving the minimum
distortion. Three hybrid digital-analog secure joint source channel coding
schemes are then proposed which achieve the minimum distortion. The first
coding scheme is based on Costa's dirty paper coding scheme and wiretap channel
coding scheme when the analog source is not explicitly quantized. The second
coding scheme is based on the superposition of the secure digital signal and
the hybrid digital-analog signal. It is shown that for the problem of
communicating a Gaussian source over a Gaussian wiretap channel with side
information, there exists an infinite family of optimum secure joint
source-channel coding scheme. In the third coding scheme, the quantized signal
and the analog error signal are explicitly superimposed. It is shown that this
scheme provides an infinite family of optimum secure joint source-channel
channel coding schemes with a variable number of binning. Finally, the proposed
secure hybrid digital-analog schemes are analyzed 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, i.e., when the actual
SNR is larger than the designed SNR.Comment: 14 Pages, 4 Figure
On the Secure Degrees-of-Freedom of the Multiple-Access-Channel
A -user secure Gaussian Multiple-Access-Channel (MAC) with an external
eavesdropper is considered in this paper. An achievable rate region is
established for the secure discrete memoryless MAC. The secrecy sum capacity of
the degraded Gaussian MIMO MAC is proven using Gaussian codebooks. For the
non-degraded Gaussian MIMO MAC, an algorithm inspired by interference alignment
technique is proposed to achieve the largest possible total
Secure-Degrees-of-Freedom (S-DoF). When all the terminals are equipped with a
single antenna, Gaussian codebooks have shown to be inefficient in providing a
positive S-DoF. Instead, a novel secure coding scheme is proposed to achieve a
positive 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. It is proven that the total S-DoF of can be
achieved for almost all channel gains. For the other channel gains, a
multi-layer coding scheme is proposed to achieve a positive S-DoF. As a
function of channel gains, therefore, the achievable S-DoF is discontinued.Comment: The conference version of this work has been submitted to ISIT 201
The Secrecy Capacity Region of the Degraded Vector Gaussian Broadcast Channel
Abstract β 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. I