6 research outputs found
Effects of Correlation of Channel Gains on the Secrecy Capacity in the Gaussian Wiretap Channel
Secrecy capacity is one of the most important characteristic of a wireless communication channel. Therefore, the study of this characteristic wherein the system has correlated channel gains and study them for different line-of-sight (LOS) propagation scenarios is of ultimate importance.
The primary objective of this thesis from the mathematical side is to determine the secrecy capacity (SC) for correlated channel gains for the main and eavesdropper channels in a Gaussian Wiretap channel as a function from main parameters (μ, Σ, ρ). f(h1, h2) is the joint distribution of the two channel gains at channel use (h1, h2), fi(hi) is the main distribution of the channel gain hi. The results are based on assumption of the Gaussian distribution of channel gains (gM, gE). The main task of estimating the secrecy capacity is reduced to the problem of solving linear partial differential equations (PDE). Different aspects of the analysis of secrecy capacity considered in this research are the Estimation of SC mathematically and numerically for correlated SISO systems and a mathematical example for MIMO systems with PDE.
The variations in Secrecy Capacity are studied for Rayleigh (NLOS) distribution and Rician (LOS) distribution. Suitable scenarios are identified in which secure communication is possible with correlation of channel gains. Also, the new algorithm using PDE has a higher speed and than analog algorithms constructed on the classical statistical Monte Carlo methods. Taking into account the normality of the distribution of system parameters, namely the channel gain (gM, gE), the algorithm is constructed for systems of partial differential equations which satisfies the secrecy criterion.
Advisor: H. Andrew Harm
Cooperation with an Untrusted Relay: A Secrecy Perspective
We consider the communication scenario where a source-destination pair wishes
to keep the information secret from a relay node despite wanting to enlist its
help. For this scenario, an interesting question is whether the relay node
should be deployed at all. That is, whether cooperation with an untrusted relay
node can ever be beneficial. We first provide an achievable secrecy rate for
the general untrusted relay channel, and proceed to investigate this question
for two types of relay networks with orthogonal components. For the first
model, there is an orthogonal link from the source to the relay. For the second
model, there is an orthogonal link from the relay to the destination. For the
first model, we find the equivocation capacity region and show that answer is
negative. In contrast, for the second model, we find that the answer is
positive. Specifically, we show by means of the achievable secrecy rate based
on compress-and-forward, that, by asking the untrusted relay node to relay
information, we can achieve a higher secrecy rate than just treating the relay
as an eavesdropper. For a special class of the second model, where the relay is
not interfering itself, we derive an upper bound for the secrecy rate using an
argument whose net effect is to separate the eavesdropper from the relay. The
merit of the new upper bound is demonstrated on two channels that belong to
this special class. The Gaussian case of the second model mentioned above
benefits from this approach in that the new upper bound improves the previously
known bounds. For the Cover-Kim deterministic relay channel, the new upper
bound finds the secrecy capacity when the source-destination link is not worse
than the source-relay link, by matching with the achievable rate we present.Comment: IEEE Transactions on Information Theory, submitted October 2008,
revised October 2009. This is the revised versio
Physical layer secrecy channel coding
Wireless communications is expanding and becoming an indispensable part of our daily life. However, due to its channel open nature, it is more vulnerable to attacks, such as eavesdropping and jamming which jeopardize the confidentiality of wireless data, compared to its counter-part, wireline communications. Security in wireless communication is thus a very important factor that should be perfected to accommodate the rapid growth of wireless communication today. Motivated by information theoretic secrecy definitions, we adopt a simple way to define the secrecy of a system by looking at its Bit-Error-Rate (BER) curves, the correlation of error vectors and Log Likelihood Ratios (LLRs) of the decoded information bits. The information bit errors and LLRs of a physical layer secure system should be uncorrelated and the BER curve should have an acceptable sharp transition from high to low BERs at prescribed signal to noise ratio (SNR) thresholds. We study catastrophic codes and Serial Concatenated Convolutional Codes (SCCC) as two candidates. For the former, we provide both detailed analytical and simulation results, to demonstrate how we can change the encoding parameters to make the resulting BER curves have the intended properties. For SCCC, we study two options. One is having a catastrophic code as an inner code. The other is to use regular SCCC. Several approaches are proposed to change the shape of the resulting BER curves. In addition, the correlation present in their information bit errors and LLRs are investigated to see how it can be used to detect or even correct errors. We find that regular SCCC codes have strong correlation in their error vectors which is captured by the associated LLRs. In low SNR regions, eavesdropper can easily make reliable decisions on which packets to drop based on LLRs, which thus undermines the security of the main channel data. On the other hand, by selecting proper outer codes, SCCC with catastrophic encoder does not have such a weakness. We conclude that Catastrophic convolutional codes, as well as serial concatenated catastrophic codes have desired properties. Therefore, they can be considered promising approaches to achieving practical secrecy in wireless systems
Physical-Layer Security in Wireless Communication Systems
The use of wireless networks has grown significantly in contemporary
times, and continues to develop further. The broadcast nature of
wireless communications, however, makes them particularly vulnerable
to eavesdropping. Unlike traditional solutions, which usually handle
security at the application layer, the primary concern of this
dissertation is to analyze and develop solutions based on coding
techniques at the physical-layer.
First, in chapter , we consider a scenario where a source node
wishes to broadcast two confidential messages to two receivers,
while a wire-tapper also receives the transmitted signal. This model
is motivated by wireless communications, where individual secure
messages are broadcast over open media and can be received by any
illegitimate receiver. The secrecy level is measured by the
equivocation rate at the eavesdropper. We first study the general
(non-degraded) broadcast channel with an eavesdropper, and present
an inner bound on the secrecy capacity region for this model. This
inner bound is based on a combination of random binning, and the
Gelfand-Pinsker binning. We further study the situation in which the
channels are degraded. For the degraded broadcast channel with an
eavesdropper, we present the secrecy capacity region. Our achievable
coding scheme is based on Cover's superposition scheme and random
binning. We refer to this scheme as the Secret Superposition Scheme.
Our converse proof is based on a combination of the converse proof
of the conventional degraded broadcast channel and Csiszar Lemma. We
then assume that the channels are Additive White Gaussian Noise and
show that the Secret Superposition Scheme with Gaussian codebook is
optimal. The converse proof is based on Costa's entropy power
inequality. Finally, we use a broadcast strategy for the slowly
fading wire-tap channel when only the eavesdropper's channel is
fixed and known at the transmitter. We derive the optimum power
allocation for the coding layers, which maximizes the total average
rate.
Second, in chapter , we consider the
Multiple-Input-Multiple-Output (MIMO) scenario of a broadcast
channel where a wiretapper also receives the transmitted signal via
another MIMO channel. First, we assume that the channels are
degraded and the wiretapper has the worst channel. We establish the
capacity region of this scenario. Our achievability scheme is the
Secret Superposition Coding. For the outerbound, we use notion of
the enhanced channels 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. We then extend the result of the
degraded case to a 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 scheme and show that it is optimal for this
channel. We then present a corollary generalizing the capacity
region of the two receivers case to the case of multiple receivers.
Finally, we investigate a scenario which frequently occurs in the
practice of wireless networks. In this scenario, the transmitter and
the eavesdropper have multiple antennae, while both intended
receivers have a single antenna (representing resource limited
mobile units). We characterize the secrecy capacity region in terms
of generalized eigenvalues of the receivers' channels and the
eavesdropper's channel. We refer to this configuration as the MISOME
case. We then present a corollary generalizing the results of the
two receivers case to multiple receivers. In the high SNR regime, we
show that the capacity region is a convex closure of rectangular
regions.
Finally, in chapter , we consider a -user secure Gaussian
Multiple-Access-Channel with an external eavesdropper. We establish
an achievable rate region for the secure discrete memoryless MAC.
Thereafter, we prove the secrecy sum capacity of the degraded
Gaussian MIMO MAC using Gaussian codebooks. For the non-degraded
Gaussian MIMO MAC, we propose an algorithm inspired by the
interference alignment technique to achieve the largest possible
total Secure-Degrees-of-Freedom . When all the terminals are
equipped with a single antenna, Gaussian codebooks have shown to be
inefficient in providing a positive S-DoF. Instead, we propose a
novel secure coding scheme 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. We use tools from the field
of Diophantine Approximation in number theory to analyze the
probability of error in the coding scheme. We prove that the total
S-DoF of can be achieved for almost all channel
gains. For the other channel gains, we propose a multi-layer coding
scheme to achieve a positive S-DoF. As a function of channel gains,
therefore, the achievable S-DoF is discontinued