29 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
Gaussian Multiple Access via Compute-and-Forward
Lattice codes used under the Compute-and-Forward paradigm suggest an
alternative strategy for the standard Gaussian multiple-access channel (MAC):
The receiver successively decodes integer linear combinations of the messages
until it can invert and recover all messages. In this paper, a multiple-access
technique called CFMA (Compute-Forward Multiple Access) is proposed and
analyzed. For the two-user MAC, it is shown that without time-sharing, the
entire capacity region can be attained using CFMA with a single-user decoder as
soon as the signal-to-noise ratios are above . A partial analysis
is given for more than two users. Lastly the strategy is extended to the
so-called dirty MAC where two interfering signals are known non-causally to the
two transmitters in a distributed fashion. Our scheme extends the previously
known results and gives new achievable rate regions.Comment: to appear in IEEE Transactions on Information Theor
Cross Layer Coding Schemes for Broadcasting and Relaying
This dissertation is divided into two main topics. In the first topic, we study the
joint source-channel coding problem of transmitting an analog source over a Gaussian
channel in two cases - (i) the presence of interference known only to the transmitter and (ii) in the presence of side information about the source known only to the
receiver. We introduce hybrid digital analog forms of the Costa and Wyner-Ziv coding schemes. We present random coding based schemes in contrast to lattice based
schemes proposed by Kochman and Zamir. We also discuss superimposed digital and
analog schemes for the above problems which show that there are infinitely many
schemes for achieving the optimal distortion for these problems. This provides an
extension of the schemes proposed by Bross and others to the interference/source
side information case. The result of this study shows that the proposed hybrid digital analog schemes are more robust to a mismatch in channel signal-to-noise ratio
(SNR), than pure separate source coding followed by channel coding solutions. We
then discuss applications of the hybrid digital analog schemes for transmitting under
a channel SNR mismatch and for broadcasting a Gaussian source with bandwidth
compression. We also study applications of joint source-channel coding schemes for
a cognitive setup and also for the setup of transmitting an analog Gaussian source
over a Gaussian channel, in the presence of an eavesdropper.
In the next topic, we consider joint physical layer coding and network coding
solutions for bi-directional relaying. We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter
and relay nodes exchange data over synchronized, average power constrained additive
white Gaussian noise channels. We propose structured coding schemes using lattices
for this problem. We study two decoding approaches, namely lattice decoding and
minimum angle decoding. Both the decoding schemes can be shown to achieve the
upper bound at high SNRs. The proposed scheme can be thought of as a joint physical
layer, network layer code which outperforms other recently proposed analog network
coding schemes. We also study extensions of the bi-directional relay for the case with
asymmetric channel links and also for the multi-hop case. The result of this study
shows that structured coding schemes using lattices perform close to the upper bound
for the above communication system models
Cooperative Strategies for Simultaneous and Broadcast Relay Channels
Consider the \emph{simultaneous relay channel} (SRC) which consists of a set
of relay channels where the source wishes to transmit common and private
information to each of the destinations. This problem is recognized as being
equivalent to that of sending common and private information to several
destinations in presence of helper relays where each channel outcome becomes a
branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and
capacity region for a set with two memoryless relay channels are investigated.
The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and
\emph{Compress-and-Forward} (CF) must be capable of transmitting information
simultaneously to all destinations in such set.
Depending on the quality of source-to-relay and relay-to-destination
channels, inner bounds on the capacity of the general BRC are derived. Three
cases of particular interest are considered: cooperation is based on DF
strategy for both users --referred to as DF-DF region--, cooperation is based
on CF strategy for both users --referred to as CF-CF region--, and cooperation
is based on DF strategy for one destination and CF for the other --referred to
as DF-CF region--. These results can be seen as a generalization and hence
unification of previous works. An outer-bound on the capacity of the general
BRC is also derived. Capacity results are obtained for the specific cases of
semi-degraded and degraded Gaussian simultaneous relay channels. Rates are
evaluated for Gaussian models where the source must guarantee a minimum amount
of information to both users while additional information is sent to each of
them.Comment: 32 pages, 7 figures, To appear in IEEE Trans. on Information Theor