15 research outputs found
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
Capacity Analysis for Gaussian and Discrete Memoryless Interference Networks
Interference is an important issue for wireless communication systems where multiple
uncoordinated users try to access to a common medium. The problem is even more
crucial for next-generation cellular networks where frequency reuse becomes ever more
intense, leading to more closely placed co-channel cells. This thesis describes our attempt to understand the impact of interference on communication performance as well as optimal ways to handle interference. From the theoretical point of view, we examine how interference affects the fundamental performance limits, and provide insights on how interference should be treated for various channel models under different operating
conditions. From the practical design point of view, we provide solutions to improve the
system performance under unknown interference using multiple independent receptions
of the same information.
For the simple two-user Gaussian interference channel, we establish that the simple
Frequency Division Multiplexing (FDM) technique suffices to provide the optimal sum-
rate within the largest computable subregion of the general achievable rate region for a
certain interference range.
For the two-user discrete memoryless interference channels, we characterize different
interference regimes as well as the corresponding capacity results. They include one-
sided weak interference and mixed interference conditions. The sum-rate capacities are
derived in both cases. The conditions, capacity expressions, as well as the capacity achieving schemes are analogous to those of the Gaussian channel model. The study
also leads to new outer bounds that can be used to resolve the capacities of several new
discrete memoryless interference channels.
A three-user interference up-link transmission model is introduced. By examining how
interference affects the behavior of the performance limits, we capture the differences
and similarities between the traditional two-user channel model and the channel model
with more than two users. If the interference is very strong, the capacity region is just
a simple extension of the two-user case. For the strong interference case, a line segment
on the boundary of the capacity region is attained. When there are links with weak
interference, the performance limits behave very differently from that of the two-user
case: there is no single case that is found of which treating interference as noise is
optimal. In particular, for a subclass of Gaussian channels with mixed interference, a
boundary point of the capacity region is determined. For the Gaussian channel with
weak interference, sum capacities are obtained under various channel coefficients and
power constraint conditions. The optimalities in all the cases are obtained by decoding
part of the interference.
Finally, we investigate a topic that has practical ramifications in real communication
systems. We consider in particular a diversity reception system where independently
copies of low density parity check (LDPC) coded signals are received. Relying only on
non-coherent reception in a highly dynamic environment with unknown interference, soft-decision combining is achieved whose performance is shown to improve significantly over existing approaches that rely on hard decision combining
SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS
We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite
element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is
accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement